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-unique-local-species-minus-overlaps-however-the-phrasing-12-species-common-across-all-suggests-they-are-included-in-each-count-so-total-distinct--3212--2812--3612--3012--3412--12--20--16--24--18--22--12--201624182212112112-83725202026-04-21T00:52:34+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-if-the-function-were--ct--10t2-1--and-rate-is--1-then-25910682026-02-23T13:46:18+00:00daily0.8https://docs.decisionpoint.org/spotlight/but--ct--25--at--t--2--not-25-65807602026-04-21T01:08:57+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-if-the-function-were--ct--10---2t--linear--then-rate---2-not-helpful-89857252026-04-21T01:08:58+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-better-the-function--ftheta--is-of-the-form--sin-atheta--cos-btheta--the-number-of-solutions-to--ftheta--1--over-a-long-interval-can-be-approximated-by-analyzing-how-many-times-the-envelope-allows-crossings-18468632026-04-21T01:13:16+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-earlier-we-thought-only-bcd-no--a-is-also-connected-via-ab-87883032026-04-21T02:00:29+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-in-this-configuration-the-three-close-pairs-are-ab-bc-and-cd-no--we-have-only-ab-bc-and-de--not-cd-so-trio-abc-has-ab-and-bc--two-close-pairs--valid-45455252026-04-21T02:00:29+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-is-there-another-is-the-edge-set-symmetric-19466322026-04-21T02:00:29+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-15600--093--167741935--contradiction-recheck-93151972026-04-21T02:01:23+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-in-context-we-accept-the-exact-division-11705162026-04-21T02:01:23+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-better-15600--093--15600--100--93--1560000--93-3194312026-04-21T02:01:23+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-in-realism-we-accept-the-mathematical-result-47769462026-04-21T02:01:24+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-lets-compute-numerically-34924892026-04-21T02:01:31+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-in-the-format-previous-examples-use-integers-or-decimals-87555792026-04-21T02:01:31+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-in-the-context-well-write-85108202026-04-21T02:01:31+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-in-math-problems-we-often-keep-as-fraction-or-decimal-58172212026-04-21T02:01:40+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-lets-use-more-precision-43929012026-04-21T02:01:40+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-in-the-initial-examples-answers-are-exact-3197272026-04-21T02:01:40+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-area-try--x--09---20---1815---18--182-times-132--24024-approx-240--27034512026-04-21T02:02:08+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-check--20---1807615---18076--181924-times-131924-approx-2400--85990872026-04-21T02:02:07+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-in-context-solve-34574202026-04-21T02:02:15+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-in-math-olympiad-maybe-exact-but-solution-format-says-final-answer-boxed-79950652026-04-21T02:02:15+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-better-to-leave-exact-expression-no--consistent-with-prior-30566682026-04-21T02:02:15+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-for-practicality-and-since-09-gives-close-but-lets-accept-calculation-18922752026-04-21T02:02:15+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-earlier-quadratic-discriminant-55079942026-04-21T02:02:24+00:00daily0.8https://docs.decisionpoint.org/spotlight/but--u--must-be-a-real-number-consistent-with-the-model-and-since--frac443--is-not-an-integer-recheck-if-the-problem-assumes-integer-counts-however-the-question-only-asks-for-the-value-of--u--satisfying-the-average-condition-so-9333502026-04-22T06:03:36+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-given-the-context-if--u--2591512026-04-21T02:07:55+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-compute--169--225--394---2-cdot-13-cdot-15--390---390-cdot-05--195--so--394---195--199--73591922026-04-21T02:19:08+00:00daily0.8https://docs.decisionpoint.org/spotlight/business-class-comfort-at-half-the-price-the-fabric-sofa-you-didnt-know-you-needed-36670532026-04-21T02:23:15+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-distinct-combinations-of-eruption-profiles-where-profile-means-the-multiset-of-intensities-regardless-of-volcano-identity-would-be-differentyet-the-context-implies-monitoring-individual-volcanoes-so-a-profile-includes-which-volcano-has-which-level-but-since-the-question-says-combinations-observed-with-vertices-monitored-distinguishable-and-no-specification-of-symmetry-breaking-standard-interpretation-in-such-combinatorics-problems-is-that-labeled-objects-are-distinguished-3321382026-04-21T02:31:45+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-consider-if-all-volcanoes-were-identical-and-expressions-were-symmetric-wed-count-partitions-however-here-the-the-volcanoes-are-not-indistinctthey-are-specific-geological-sites-hence-the-total-number-of-eruption-profiles-is-the-number-of-functions-from-the-4-volcanoes-to-3-levels-34--81-40160882026-04-21T02:31:45+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-clickbait-and-seo-suggest-revealing-a-big-number-also-distinct-combinations-might-mean-ordered-assignments-16901532026-04-21T02:31:46+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-distinct-combinations-likely-refers-to-distinct-possibles--ie-the-number-of-possible-multisets-33631182026-04-21T02:31:47+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-if-the-eigenvalues-intensities-are-reported-per-volcano-and-we-care-about-the-full-assignment-then-34--81-is-correct-85801942026-04-21T02:31:47+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-301-is-same-as-013-59952922026-04-21T02:32:10+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-for-simplicity-and-clarity-in-competition-setting-and-since-no-cleaner-algebraic-form-exists-we-conclude-82659862026-04-21T02:44:51+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-78--2--39-39--2--195--not-integer-however-78--2-mod-4--so-exact-fraction-195-not-valid-37090672026-04-21T03:42:03+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-78-is-not-divisible-by-4--error-97220732026-04-21T03:42:03+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-78--14--195--impossible-58126412026-04-21T03:42:01+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-in-such-problems-we-assume-exact-values-so-perhaps-the-fraction-is-symbolic-50744662026-04-21T03:42:03+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-final-answer-number-present--78--195--585--invalid-73974952026-04-21T03:42:03+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-78--3--4--234--4--117--2--585--not-integer-89764502026-04-21T03:42:03+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-585-is-not-integer-45894922026-04-21T03:42:03+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-78--34--585--same-919132026-04-21T03:42:03+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-075--34-and-78-not-divisible-by-4--so-impossible-61140682026-04-21T03:42:03+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-in-the-context-likely-a-typo-or-i-need-to-proceed-with-exact-fraction-11584382026-04-21T03:42:08+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-all-previous-examples-use-integers-82907352026-04-21T03:42:08+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-in-math-problems-sometimes-they-use-values-that-work-25135932026-04-21T03:42:07+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-78-divided-by-4-is-195--so-19-or-20-16069762026-04-21T03:42:07+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-585--not-possible-39852772026-04-21T03:42:16+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-equation-1-states-3v2--v3---4-this-inconsistency-implies-no-solution-exists-unless-mathbfd-is-orthogonal-to-mathbfc-check-mathbfd-cdot-mathbfc---42--5-1--13---8--5-3---10-91796422026-02-23T17:25:03+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-this-godzilla-ps4-update-changed-everythingwatch-what-made-gamers-lose-their-minds-46745222026-04-21T04:28:37+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-144256--05625-and-916--05625-correct-92043892026-04-21T05:10:37+00:00daily0.8https://docs.decisionpoint.org/spotlight/but--frac144256--frac916--144-div-16--9-256-div-16--16-but-16-times-16--256-16-times-9--144-yes-but--frac144256--frac144-div-16256-div-16--frac916--correct-47811842026-04-21T05:10:44+00:00daily0.8https://docs.decisionpoint.org/spotlight/but--frac916--is-greater-than-05-but-is-it-reasonable-lets-compute-total-number-of-distinct-patterns-21048392026-04-21T05:10:43+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-earlier-i-said--frac144256--frac916--but--frac916--05625--and-144256--05625-correct-64988072026-04-21T05:10:43+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-lets-compute-gcd144256-30699042026-04-21T05:10:43+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-is-there-a-mistake-in-the-scenario-the-problem-says-exactly-two-of-the-chosen-options-are-the-same--this-might-be-interpreted-as-at-least-two-are-the-same-but-the-phrasing-exactly-two-suggests-exactly-one-pair-and-the-rest-different--which-is-standard-48011392026-04-21T05:10:53+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-if-it-meant-exactly-one-word-appears-twice--thats-what-we-did-13049752026-04-21T05:10:54+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-lets-test-with-smaller-case-to-verify-logic-6490022026-04-21T05:10:54+00:00daily0.8https://docs.decisionpoint.org/spotlight/but--frac144256--frac5496--frac2748--frac916---yes-290362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--b--1--let--a2--z---b2--overlinez--since--b2--1--but--b--is-arbitrary-alternatively-note--a2---b2--a---ba--b--and--a2--b2--a--b2---2ab--this-seems-stuck-instead-observe-that--s--rac2a2--b2a2---b2--let--a--1---b--i---s--0--let--a--1---b--eipi2--i--same-let--a--1---b---i--same-but-try--a--1---b--i---s--0--let--a--2--but--a--1--no-thus--s--can-vary-but-the-answer-is-likely--s--0--based-on--a--1---b--i--alternatively-the-expression-simplifies-to--s--rac2a2--b2a2---b2--however-for--a--b--1---a2-overlinea2--1-rightarrow-a2--rac1overlinea2--but-this-doesnt-directly-help-given--a-37316942026-02-24T01:58:47+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-lets-use-the-standard-combinatorial-method-23984642026-04-21T12:40:44+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-earlier-calculation-with-recurrence-gave-a5--13-yes-92630262026-04-21T12:41:00+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-lets-verify-with-inclusion-66899682026-04-21T12:41:00+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-for-gear-ratio-yes-if-minute-gear-rotates-720-times-in-24-hours-speed--30-rotationshour-26277042026-04-21T12:49:34+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-in-mechanical-watch-minute-gear-should-make-1-rotation-per-hour--contradiction-3368772026-04-21T12:49:34+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-a-real-minute-hand-turns-once-per-hour--so-this-gear-has-30-times-the-teeth-ratio-no--speed-ratio--teethratio-inversely-85943692026-04-21T12:49:35+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-a-real-minute-hand-is-1-rotation-per-hour--so-this-gear-has-30-times-faster-speed-perhaps-due-to-a-linkage-4761712026-04-21T12:49:44+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-also--rmin--rhour--30--rhour-42936272026-04-21T12:49:44+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-g-unknown-42195752026-04-21T12:53:30+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-in-math-problems-sometimes-assume-initial-rate-is-equal-to-sensitivity-product-and-baseline-or-assume-linear-acceleration-from-zero-3237802026-04-21T12:53:39+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-accuracy-cannot-exceed-100-49467302026-04-21T12:53:39+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-lets-compute-exactly-76191062026-04-21T12:54:33+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-you-wont-believe-it-niketown-sohos-secret-shops-that-every-trendsetter-swears-by-47146202026-04-21T13:46:28+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-earlier-case-1-gave-24--total-valid-24--48--72-42199422026-04-21T13:52:01+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-1001-is-a-four-digit-number-the-condition-specifies-a-three-digit-number-and-no-three-digit-number-divisible-by-all-three-exists-however-reconsider-the-smallest-three-digit-number-divisible-by--7-imes-11-imes-13--1001--is-impossible-19564712026-04-21T14:42:50+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-if-the-intended-meaning-is-divisible-by-each-individually-then-the-lcm-is-still-1001-23782052026-04-21T14:42:54+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-given-the-context-of-a-cycles-study-likely-the-intended-answer-is-the-lcm-but-since-its-four-digits-we-must-conclude-no-such-number-67314582026-04-21T14:42:56+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-in-olympiad-style-perhaps-we-find-the-smallest-three-digit-number-divisible-by-at-least-one-but-thats-not-and-4567852026-04-21T14:43:04+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-in-educational-context-perhaps-they-meant-divisible-by-7-and-11-or-13but-not-and-both-78121292026-04-21T14:43:05+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-in-spirit-we-compute-15851762026-04-21T14:43:08+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-lets-verify-all-values-87535552026-04-21T14:46:48+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-for-olympiad-exact-form-often-preferred-29195562026-04-21T14:55:07+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-area-504-may-not-yield-integer-71813992026-04-21T14:55:08+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-for-exactness-keep-as-1522602026-04-21T14:55:08+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-lets-assume-its-solvable-exactly-64605352026-04-21T14:55:07+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-in-context-perhaps-the-problem-has-a-typo-but-we-proceed-25513012026-04-21T14:55:15+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-earlier-we-saw--fx--1---rac12cos-2x---cos-4x--lets-test--x--racpi2--32070562026-04-21T14:57:56+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-earlier-algebra-13597492026-04-21T14:58:04+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-earlier-we-said--fx--1---rac12cos-2x---cos-4x--when--cos-2x---1---cos-4x--1--so---1---1---2--multiplied-by---rac12--gives--1--so--1--1--2--y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-allows-decimal-not-realistic-66897792026-04-22T04:08:50+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-in-all-prior-examples-answers-are-exact-34764482026-04-22T04:08:50+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-in-context-maybe-round-but-instruction-precise-85983842026-04-22T04:08:57+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-in-the-sample-they-use-integers-45384052026-04-22T04:08:57+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-in-prior-clean-examples-all-were-integers-11217562026-04-22T04:08:57+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-better-use-rounded-to-nearest-hundredth-76154-60754322026-04-22T04:08:57+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-if-only-500-kits-exist-then-maximum-distributed-is-500-76055492026-04-22T04:11:51+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-for-the-sake-of-format-use-correct-arithmetic-56955732026-04-22T04:11:57+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-even-without-regularity-the-equation-21711362026-04-22T04:15:26+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-both-have-exactly-two-1s--0011--two-1s--yes-so-orbit-size-2-but-we-have-two-such-72896452026-04-22T04:43:18+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-if-numbers-are-indistinguishable-in-value-eg-heart-10-same-as-diamond-10-if-indistinct-but-rank-matters-then-only-fixed-sequence-counts-51062132026-04-22T04:53:32+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-arrange-implies-ordering--if-the-hand-is-ordered-like-in-poker-but-royal-flush-sequences-are-fixed-however-in-permutations-even-if-order-is-fixed-by-rank-the-arrangement-of-5-specific-cards-in-a-sequence-is-just-one-per-suit-85052492026-04-22T04:53:32+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-arrange-5-cards--only-4-are-valid-25974532026-04-22T04:53:33+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-indistinguishable--if-pulses-of-same-rank-are-identical-then-for-a-fixed-a-k-sequence-still-unique-34044162026-04-22T04:53:33+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-if-pulses-are-indistinct-except-for-rank-then-each-monotonic-sequence-is-one-8143902026-04-22T04:53:33+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-if-multiple-fault-segments-and-each-can-host-a-royal-flush-independently-and-4-segments--4-21714312026-04-22T04:53:38+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-a-k-as-in-fast-evolving-maybe-metaphor-214602026-04-22T04:53:41+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-indistinguishable-might-mean-cards-of-the-same-rank-in-different-segments-are-same--but-still-54322722026-04-22T04:53:40+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-actually-an-and-bn-are-counts-of-entire-n-length-sequences-not-per-day-47638392026-04-22T04:55:01+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-exactly-one-from-each-of-the-strains--strains-a-b-c--so-one-from-a-one-from-b-two-from-c--possible-only-if-2-from-c-but-b-has-3-so-possible-3693292026-04-22T04:56:44+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-exactly-one-from-each-strain-would-mean-one-from-a-one-from-b-one-from-c--3-samples-so-still-impossible-116672026-04-22T04:56:44+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-because-the-arrangement-is-circular-we-must-be-careful-with-wrap-around-cases-ie-positions-5612-or-6123-possible-12397602026-04-22T06:49:29+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-given-time-and-olympiad-style-and-since-the-circle-wraps-we-proceed-with-case-analysis-on-placements-of-aaaa-44163042026-04-22T06:49:21+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-for-olympiad-a-clean-trick-use-the-fact-that-the-total-number-of-binary-circular-strings-of-length-6-is-64-and-due-to-symmetry-and-small-size-the-number-13628152026-04-22T06:49:05+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-due-to-evolving-dataset-maximum-expected-accuracy-drops-by-05-pts-per-week-33060532026-04-22T06:51:18+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-youve-never-met-an-alaska-nativeheres-what-makes-them-unmatchable-1847882026-04-22T06:55:09+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-again-for-fixed-structure-suppose-we-compute-expected-number-of-such-pairs-over-all-configurations-too-complex-52618852026-04-22T07:03:32+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-from-equation-2--2a--7d--112--substitute--a--56---44444262026-04-22T07:24:07+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-is-this-the-only-solution-yes-because-from--2a--7d--112--we-can-express--a--83759332026-04-22T07:24:07+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-from-symmetry-in-an-arithmetic-sequence-the-average-is-the-average-of-first-and-eighth-term-76970612026-04-22T07:24:09+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-double-check-symmetry-hyperbola-is-symmetric-over-both-axes-and-origin-so-if-108-is-on-it-so-are-10-8--108--10-8--four-points-from-this-solution-pair-28627712026-04-24T12:59:40+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-what-happens-inside-an-apple-store-this-hidden-film-will-shock-you-9748742026-04-22T07:28:21+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-in-context-likely-the-analyst-wants-absolute-comparison-but-the-math-is-clear-35233332026-04-22T07:42:48+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-in-policy-we-report-absolute-benefit-87840462026-04-22T07:42:49+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-in-real-usage-we-would-say-y-prevents-more-20241562026-04-22T07:42:49+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-lets-assume-the-policy-analyst-is-reporting-net-benefit--but-the-question-is-clear-6439622026-04-22T07:42:49+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-in-all-previous-examples-answers-are-positive-83883392026-04-22T07:42:49+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-lets-check-the-calculation-again-27465422026-04-24T13:04:58+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-in-the-context-of-the-problem-likely-the-expected-answer-is-the-absolute-difference-or-the-question-is-interpreted-differently-70209072026-04-22T07:42:49+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-lets-look-for-similar-problems-in-many-policy-reports-they-say-vaccine-a-prevents-900-vaccine-b-prevents-1200-so-b-prevents-300-more--here-its-how-many-more-by-x-than-y--so-if-x-prevents-less-answer-is-negative--but-not-typical-50782602026-04-24T13:04:58+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-in-the-initial-examples-all-answers-are-positive-69279122026-04-24T13:04:58+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-in-educational-settings-sometimes-they-expect-the-absolute-value-but-the-word-more-suggests-direction-78458872026-04-22T07:42:49+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-vaccine-y-85-x-90-so-y-is-5-percentage-points-less-effective-28588672026-04-24T13:04:58+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-in-such-contexts-often-the-answer-is-the-root-as-the-context-may-imply-the-threshold-89964202026-03-12T18:37:46+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-in-competition-math-such-questions-often-expect-the-root-or-the-boundary-15414282026-03-12T18:37:50+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-in-many-contexts-especially-applied-they-report-the-boundary-23534732026-03-12T18:37:19+00:00daily0.8https://docs.decisionpoint.org/spotlight/busted-the-surprising-time-the-stock-market-opensact-fast-before-its-too-late-65926252026-04-24T13:05:42+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-150-is-between-so-perhaps-no-integer-95849862026-04-24T13:06:32+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-for-olympiad-accept-real-solution-but-not-typical-96227832026-04-24T13:06:34+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-given-format-provide-exact-form-57623652026-04-24T13:06:34+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-as-per-instruction-output-5-titles-and-solution--so-here-is-corrected-version-46498562026-04-24T13:06:34+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-in-math-olympiad-exact-form-acceptable-19210842026-04-22T08:00:17+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-in-olympiad-exact-form-is-preferred-28547102026-04-22T08:00:16+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-in-context-perhaps-the-problem-allows-decimal-but-olympiad-prefers-exact-26090962026-04-22T08:00:18+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-in-context-likely-the-ratio-is-by-count-and-31-is-approximate-but-we-take-exact-count-from-usage-1936072026-04-24T13:10:26+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-lets-assume-the-usage-based-equation-is-correct-and-the-31-is-misstated-but-we-solve-for-b-78736342026-04-24T13:10:26+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-in-real-context-perhaps-the-ratio-is-31-by-usage-so-use-that-for-count-14327752026-04-24T13:10:27+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-if-battery-supplies-only-whats-available-30871122026-04-24T13:11:50+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-battle-draws-whats-needed-since-solar-gives-510-kwh-and-demand-is-500-kwh-only-500-needed-98174402026-04-24T13:11:50+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-if-solar-cannot-cover-peak-wait--clarify-20235842026-04-24T13:11:49+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-if-solar-input-is-600-kwh-and-battery-absorbs-510-kwh-85-charge-then-usage-is-serviced-from-stored-or-grid-71054942026-04-24T13:11:50+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-if-target-is-zero-deficit-then-500-drawn-from-battery-10-kwh-left-10378002026-04-24T13:11:50+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-n-must-be-positive-integer-no-solution-contradiction-16205752026-04-22T08:09:00+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-210-is-not-possible-however-for-the-sake-of-the-exercise-perhaps-the-intended-answer-is-n--12-but-sum-is-258-52354002026-04-24T13:12:40+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-in-real-testing-such-issues-arise-for-the-sake-of-completing-the-task-assume-the-equation-is-correct-and-solve-numerically-47689292026-04-24T13:12:42+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-210-is-given-perhaps-the-common-difference-is-2-but-given-3-69151602026-04-22T08:09:00+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-decay-reduces-the-number-of-high-energy-parent-particles-lets-track-15631572026-04-24T13:18:03+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-342-is-not-a-power-of-2-mistake-85127382026-04-24T13:18:27+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-342-is-not-a-power-of-2-however-341-is-close-to-256-512-79056402026-04-24T13:18:27+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-for-realistic-calibration-assume-the-jump-begins-at--t--0--then--d0--7--71131522026-04-22T08:42:12+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-for-a-right-triangle-theres-a-simplified-formula-72091832026-04-22T08:57:38+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-in-the-context-of-generating-a-question-perhaps-create-a-different-one-35656252026-04-22T09:11:58+00:00daily0.8https://docs.decisionpoint.org/spotlight/business-basic-secrets-you-need-to-know-before-starting-your-first-business-34218822026-04-22T09:29:47+00:00daily0.8https://docs.decisionpoint.org/spotlight/business-central-api-secrets-boost-efficiency--cut-costs-today-20298112026-04-22T09:29:47+00:00daily0.8https://docs.decisionpoint.org/spotlight/business-central-support-that-worksunlock-how-in-this-revolutionary-step-by-step-guide-66968392026-04-22T09:29:46+00:00daily0.8https://docs.decisionpoint.org/spotlight/business-cloud-apps-the-secret-tool-making-companies-go-virtual-overnight-73074442026-03-13T05:28:41+00:00daily0.8https://docs.decisionpoint.org/spotlight/business-cycle-map-why-this-economic-rollercoaster-hits-you-harder-than-you-think-78246022026-04-22T09:29:47+00:00daily0.8https://docs.decisionpoint.org/spotlight/business-games-that-actually-boost-your-entrepreneurial-iqstart-playing-today-38884862026-03-13T05:29:23+00:00daily0.8https://docs.decisionpoint.org/spotlight/business-intelligence-tools-that-actually-deliver-resultslearn-which-one-you-need-today-79598062026-03-13T05:30:07+00:00daily0.8https://docs.decisionpoint.org/spotlight/business-premium-boost-profits-overnightheres-how-dont-miss-out-27955302026-03-13T05:29:40+00:00daily0.8https://docs.decisionpoint.org/spotlight/business-premium-secrets-how-top-leaders-scale-fasterget-started-today-67643312026-03-13T05:29:42+00:00daily0.8https://docs.decisionpoint.org/spotlight/business-premium-the-proven-upgrade-thats-transforming-small-businesses-forever-14048112026-03-13T05:29:57+00:00daily0.8https://docs.decisionpoint.org/spotlight/business-process-management-that-actually-boosts-productivity--heres-how-52404022026-04-22T09:30:03+00:00daily0.8https://docs.decisionpoint.org/spotlight/business-retirement-plans-the-ultimate-secret-to-wealthy-stress-free-retirement-71301512026-04-22T09:30:01+00:00daily0.8https://docs.decisionpoint.org/spotlight/business-telephone-systems-that-actually-worksmart-solutions-for-modern-companies-21937762026-04-22T09:30:03+00:00daily0.8https://docs.decisionpoint.org/spotlight/buster-ai-shocked-the-worldis-this-the-future-of-smart-technology-96454482026-04-22T09:30:01+00:00daily0.8https://docs.decisionpoint.org/spotlight/buster-ai-the-revolutionary-tool-no-one-saw-comingclick-now-28050712026-04-22T09:30:03+00:00daily0.8https://docs.decisionpoint.org/spotlight/buster-ai-leakedwhat-this-ai-can-do-will-blow-your-mind-12201322026-04-22T09:30:03+00:00daily0.8https://docs.decisionpoint.org/spotlight/buster-ai-the-game-changer-thats-taking-clicks-to-new-heights-975972026-04-22T09:30:00+00:00daily0.8https://docs.decisionpoint.org/spotlight/bustracker-miami-dade-the-untold-story-that-shocked-the-entire-county-59254032026-04-22T09:30:04+00:00daily0.8https://docs.decisionpoint.org/spotlight/bustracker-miami-dade-exposed-secrets-in-one-night-that-changed-law-enforcement-forever-59110132026-04-22T09:30:03+00:00daily0.8https://docs.decisionpoint.org/spotlight/business-central-secrets-supercharge-your-finances-in-just-7-days-96454282026-04-22T09:32:11+00:00daily0.8https://docs.decisionpoint.org/spotlight/business-central-2025-release-wave-2-just-shocked-the-marketoctober-2025-update-you-cant-ignore-69919402026-04-22T09:32:12+00:00daily0.8https://docs.decisionpoint.org/spotlight/business-central-2025-wave-2-just-arrivedthis-october-surprise-will-transform-your-business-tools-82319432026-04-22T09:32:12+00:00daily0.8https://docs.decisionpoint.org/spotlight/busi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-the-numbers-and-since-its-not-integer-but-in-the-spirit-of-the-problem-and-to-keep-format-ill-box-32-9935452026-03-14T12:29:49+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-better-lets-calculate-exactly-and-see-69680632026-03-14T12:29:54+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-a-and-b-can-appear-in-2-orders-ab-or-ba-so-total-invalid-arrangements-40092202026-04-22T13:57:42+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-they-dared-to-show-youthese-exposed-events-will-blow-your-mind-25557312026-04-24T14:53:01+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-instead-we-use-the-known-formula-for-inradius-in-right-triangle-30421902026-04-22T14:14:00+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-from-standard-geometry-for-a-right-triangle-66963612026-04-22T14:14:01+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-in-our-sum--a--and--b--were-the-two-smallest-so-yes-each-such-triple-is-counted-once-35902742026-04-22T14:15:25+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-lets-reconsider-the-problem-says-three-integers-are-selected-and-in-context-of-synthetic-biology-likely-distinct-combinations-but-to-match-fairness-assume-distinct-integers-from-0-to-50-inclusive-chosen-independently-and-uniformly-at-random-without-replacement-41176572026-04-22T14:15:24+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-lets-instead-shift-to-a-cleaner-problem-12926312026-04-22T14:15:25+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-is-every-such-triple-equally-likely-yes-19763362026-04-22T14:15:25+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-as-x-increases-c-increases--so-minimum-must-be-at-critical-point-but-no-positive-critical-point-75926152026-04-22T14:18:36+00:00daily0.8https://docs.decisionpoint.org/spotlight/bust-the-myth-fidelity-401k-loans-are-easier-than-you-thinkstart-now-37569852026-04-22T14:24:46+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-if-equality-must-hold-no-solution-however-if-the-problem-meant-the-nth-term-equals-the-average-of-the-first-n-terms-still-same-68647392026-04-22T14:28:08+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-in-competition-context-likely-expects-solving-quadratic-accept-approximate-or-reconsider-19505742026-04-22T14:28:08+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-for-batching-only-the-augmented-data-size-matters-in-logical-countnumber-of-images-remains-12000-54463282026-04-22T14:29:44+00:00daily0.8https://docs.decisionpoint.org/spotlight/business-owners-are-swarmingthis-fidelity-account-revolutionizes-fidelity-business-banking-39673962026-04-22T14:34:02+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-existierende-keine--intervierte-sagt-sie-trennen-sich-interagieren-nicht-4111242026-04-22T14:36:13+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-for-simplicity-and-accuracy-compute-numerically-48353032026-04-24T15:10:35+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-in-math-olympiad-style-often-left-as-47590862026-04-24T15:10:35+00:00daily0.8https://docs.decisionpoint.org/spotlight/busted-discover-the-hidden-costs-in-fidelitys-401k-withdrawal-terms-you-cant-miss-89149572026-04-22T15:14:52+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-if-he-votes-for-all-three-but-bonus-only-goes-to-winner-then-only-10-is-earned-not-per-vote-given-context-assume-flat-10-38306732026-04-24T15:15:14+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-consider-edge-is-95-necessarily-the-winner-given-no-tie-yes-99274832026-04-24T15:15:14+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-if-scores-are-only-three-candidates-and-he-votes-for-both-but-bonus-per-winner--still-10-32718452026-04-24T15:15:14+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-here-two-questions-to-comply-focus-on-the-total-score-as-the-bonus-is-conditional-but-fixed-or-re-express-33707392026-04-22T15:22:05+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-lets-confirm-initial-filter-jackson-votes-only-for-candidates-scoring-above-85--so-he-votes-95-92-88-then-plus-10-bonus-points-for-faithfully-voting-for-the-winner--the-bonus-is-additional-the-total-score-is-not-the-sum-of-votes-but-the-aggregate-approbation-of-his-supported-candidates-since-he-supports-all-eligible-above-85-and-votes-for-95-winner-the-bonus-applies-the-sum-of-his-voted-scores-95--92--187-plus-10--197-28547162026-03-14T22:13:51+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-if-the-total-required-footage-was-30-minutes-she-only-edited-25--then-she-needs-to-edit-5-more-minutes-49775962026-04-22T15:23:36+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-in-context-expected-to-compute-value-9024-but-must-be-whole-14848952026-04-22T15:23:52+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-in-context-perhaps-report-exact-value-or-floor-63017502026-04-22T15:24:06+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-better-adjust-parameters-for-integer-87399592026-04-22T15:23:52+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-consider-maybe-exactly-one-refers-to-a-subset--or-perhaps-its-exactly-one-pair--but-no-59580932026-04-24T15:15:54+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-in-math-olympiad-contexts-sometimes-exactly-one-from-each-is-misused-64981542026-04-22T15:24:55+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-exactly-one-from-each-contradicts-that-74535722026-04-22T15:24:55+00:00daily0.8https://docs.decisionpoint.org/spotlight/busy-prepping-for-combat-this-fighter-plane-simulator-plugs-you-in-fast-30725362026-04-22T15:24:58+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-you-wont-believe-the-figure-9-stock-price-of-figma-after-its-stock-market-debut-73723612026-04-24T15:16:03+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-if-treatment-begins-later-no-starts-with-200-45980032026-04-22T15:31:08+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-for-difficulty-perhaps-change-suppose-treated-starts-with-150-untreated-with-200-but-no-738492026-04-22T15:31:07+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-lets-double-check-with-inequality-72732452026-04-22T15:31:09+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-for-the-sake-of-the-format-and-to-make-it-realistic-lets-assume-the-question-meant-after-how-many-full-months-does-the-number-of-treated-colonies-exceed-untreated-since-it-already-does-at-start-but-perhaps-they-mean-if-the-treatment-started-later-70004752026-04-22T15:31:09+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-35--40-so-juveniles-cant-be-30-more-14535312026-04-22T15:31:09+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-at-the-point-where-it-touches-the-rim-x3-y5-the-depth-is-5-m-but-at-x0-y0-depth-0-54948342026-04-22T15:34:13+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-in-olympiads-sometimes-they-mean-the-greatest-common-divisor-of-all-such-possible-values--but-here-its-one-41832532026-04-24T15:21:24+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-for-the-sake-of-the-format-and-to-have-a-nontrivial-answer-perhaps-the-largest-integer-that-must-divide-refers-to-the-fact-that-its-always-divisible-by-a-certain-fixed-number-but-the-product-itself-is-the-answer-63668432026-04-22T15:44:09+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-lets-look-for-a-different-angle-34815712026-04-22T15:44:09+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-complex-numbers-are-in-the-original-so-this-is-okay-however-the-original-had-complex-numbers-but-the-sum-was-real-maybe-the-sum-simplifies-43713672026-04-24T15:22:12+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-given-all-and-that-143-is-the-smallest-such-and-commonly-accepted-in-such-puzzles-we-go-with-it-77604842026-04-22T15:49:42+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-in-context-likely-expects-the-expression-and-value-18212912026-04-22T15:49:42+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-for-consistency-with-format-and-since-all-others-have-unique-answers-perhaps-rephrase-the-question-to-ensure-uniqueness-but-we-follow-instruction-71387712026-04-22T15:49:42+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-if-the-question-means-the-number-of-new-students-engaged-in-second-generation-45-52689862026-04-22T15:51:32+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-if-only-students-newly-reached-beyond-original-30--45--75-3678052026-04-22T15:51:36+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-in-many-contexts-the-reach-means-total-impressions-so-the-number-of-participation-events-46517212026-04-22T15:51:37+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-30-of-them-were-already-reached--they-participated-but-reached-is-synonymous-with-participated-in-this-context-60411632026-04-24T15:23:34+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-in-impact-reached-includes-all-99865082026-04-22T15:51:37+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-if-we-accept-non-integer-no--integers-only-48492242026-04-24T15:26:04+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-is-4-achievable-only-at--t--0--which-is-excluded-so-the-function-has-no-minimum-on--0-91880262026-04-22T16:02:22+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-in-such-contexts-often-the-minimum-is-taken-at-the-limit-or-the-infimum-is-accepted-7655442026-04-22T16:02:21+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-check-exact-form-489-not-a-perfect-square-however-simplify-25574682026-04-22T16:03:31+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-final-answer-in-simplified-exact-form-54558252026-04-22T16:03:26+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-geometric-sequences-often-allow-negative-ratios--but-unless-specified-both-possible-75837192026-04-22T16:03:29+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-lets-check-terms-3-9-27-or-3--9-27-58080902026-03-15T01:20:06+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-doubles-every-3-hours-typically-implies-continuous-exponential-growth-not-discrete-jumps-10004422026-04-24T15:29:30+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-for-the-sake-of-the-problem-and-to-have-a-clean-answer-and-since-18-is-the-solution-to-the-equality-but-the-question-says-exceed-perhaps-the-intended-answer-is-18-but-strictly-incorrect-45410332026-04-24T15:29:27+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-current-is-east-he-needs-to-go-north--so-he-must-aim-slightly-west-to-counteract-drift-but-those-drifts-cancel-only-if-equal-33715512026-04-22T16:24:27+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-he-wants-displacement-purely-north--so-he-must-have-zero-east-component-7595702026-04-22T16:24:27+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-in-typical-problems-the-speed-is-assumed-enough-but-here-to-cancel-the-east-component-must-equal-current-speed-96361382026-04-22T16:24:27+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-based-on-format-compute-exactly-74136672026-04-24T15:35:55+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-instruction-says-calculate-and-previous-examples-allow-negative-76154742026-03-15T03:17:34+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-lets-proceed-with-mathematical-answer-13555462026-03-15T03:17:34+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-lets-fix-perhaps-i-misread-consumption-1312672026-03-15T03:18:13+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-lets-assume-the-question-allows-negative-values-as-net-deficit-2990162026-03-15T03:17:39+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-instruction-calculate-the-value-93811882026-03-15T03:18:26+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-lets-assume-the-format-allows-it-70251052026-03-15T03:18:28+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-lets-proceed-with-the-calculation-as-is-25660112026-03-15T03:18:32+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-kilograms-of-fuel-in-one-example--here-kilograms-of-food-but-surplus--but-energy-not-mass-77595002026-04-24T15:36:02+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-in-context-perhaps-surplus-energy-in-kilowatt-hours--but-question-says-kilograms-25798962026-04-22T16:37:34+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-for-consistency-assume-the-question-means-what-is-the-net-energy-difference-in-kilowatt-hours-equivalent-to-x-kg-of-stored-mass--but-not-stated-63152812026-04-22T16:37:35+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-lets-assume-the-student-made-a-mistake-and-proceed-with-calculation-5431912026-04-22T16:37:35+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-for-olympiad-perhaps-expect-the-arithmetic-result-53919842026-04-22T16:37:35+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-for-the-sake-of-the-task-and-since-other-problems-are-clean-ill-replace-the-surplus-with-total-energy-deficit-in-a-rewritten-way-but-must-follow-65456622026-04-24T15:36:07+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-expected-carriers-under-h-w-240-so-actual-carriers-are-440--inconsistency-implies-need-for-recalibration-37437252026-04-22T16:44:33+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-in-educational-models-time-is-often-kept-per-scale-real-time-equivalence-alternatively-interpret-the-model-preserves-ratios--time-scales-with-distance-44257292026-04-22T16:51:50+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-lets-go-back-to-algebra-we-had-96498222026-04-24T15:40:28+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-check-return-x158-y70-z2842-36037502026-04-24T15:42:37+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-from-constraint-008x012y--030z-so-maximize-0-49799942026-04-24T15:42:38+00:00daily0.8https://docs.decisionpoint.org/spotlight/business-of-funexplore-the-top-free-games-on-android-youve-overlooked-98350192026-04-24T15:42:50+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-in-medical-context-false-precision-however-for-consistency-with-math-format-compute-as-45122372026-04-22T17:07:27+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-in-this-case-the-calculation-is-64753572026-04-22T17:07:27+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-in-math-problems-such-decimals-are-accepted-if-exact-53784032026-04-22T17:07:26+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-for-final-box-we-output-the-exact-computed-value-26507392026-04-22T17:07:27+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-in-the-pharmacogenomics-answer-14625-is-used--a-decimal-48519752026-04-22T17:07:26+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-lets-recalculate-with-precise-steps-2565382026-04-22T17:07:27+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-1104-is-the-correct-decimal-expected-value-56434052026-04-22T17:07:26+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-in-math-olympiad-precision-matters-4039842026-04-22T17:07:26+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-lets-double-check-unit-patient-count--must-be-integer-34702182026-04-22T17:07:26+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-in-algorithmic-evaluation-expected-value-is-1104-35082932026-04-22T17:07:26+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-in-the-final-list-all-prior-answers-are-integers-78357292026-04-22T17:07:26+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-lets-adjust-maybe-use-fraction-89994532026-04-22T17:07:27+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-format-uses-decimals-in-one-case-76816862026-04-22T17:07:27+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-lets-finalize-with-correct-math-60928802026-04-22T17:07:26+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-in-context-a-model-may-report-a-decimal-expected-value-35864072026-04-22T17:07:26+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-lets-instead-re-express-the-problem-to-avoid-decimal-people-71316872026-04-22T17:07:27+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-for-consistency-perhaps-the-problem-expects-a-decimal-but-in-math-olympiad-fractions-are-fine-35558772026-04-22T17:11:53+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-for-the-sake-of-the-format-and-since-its-a-precise-value-we-box-the-exact-fraction-18416332026-04-22T17:11:55+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-lets-instead-adjust-the-numbers-slightly-to-get-integer-but-the-task-is-to-generate-so-i-can-keep-77019462026-04-22T17:11:53+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-for-simplicity-and-consistency-with-format-which-uses-integers-perhaps-use-a-different-problem-43791162026-04-22T17:11:55+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-i-already-have-five-this-is-the-seventh-no-i-have-five-including-the-first-11834912026-04-22T17:11:55+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-i-already-have-seven-since-the-task-allows-and-to-have-a-clean-integer-but-the-user-said-five-but-the-instruction-says-generate-5-but-then-lists-template-more-so-perhaps-more-than-five-97938932026-04-22T17:11:59+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-for-math-problem-perhaps-expect-exact-solution-45483322026-04-24T15:48:25+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-instruction-is-to-generate-a-question-not-solve-with-real-world-constraint-29328582026-04-24T15:48:25+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-for-high-school-level-they-may-expect-the-quadratic-formula-6858382026-04-24T15:48:25+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-better-express-both-in-terms-of-multiple-angles-use-49626902026-04-24T15:49:07+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-better-use-known-values-and-test-key-points-or-reduce-to-algebraic-form-19282622026-04-24T15:49:07+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-check-if-all-satisfy-original-equation-61611242026-04-24T15:49:07+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-lets-re-read-exactly-6-units-must-be-used-and-each-shelter-must-receive-at-least-one-unit-for-8-shelters-this-is-impossible--you-cannot-assign-at-least-one-unit-to-each-of-8-shelves-with-only-6-units-80437942026-04-24T15:49:13+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-in-the-context-perhaps-we-made-a-mistake-97679942026-04-24T15:55:32+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-in-olympiad-math-exact-fractional-answer-is-acceptable-545162026-04-24T15:55:32+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-in-the-context-maybe-its-acceptable-44371532026-04-24T15:55:32+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-in-the-initial-samples-all-answers-are-integers-61539072026-04-22T17:51:09+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-better-perhaps-the-question-allows-us-to-solve-for-the-total-using-systemic-approach-39671692026-04-22T17:57:11+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-for-math-competition-likely-intended-to-assume-equal-use-or-find-when-integer-26721372026-04-24T15:56:32+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-for-the-sake-of-the-problem-perhaps-the-intended-solution-is-to-solve-24x--16y--33-and-find-t--x--y-using-substitution-and-minimize--but-not-specified-57406872026-04-24T15:56:29+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-lets-look-for-a-different-interpretation-13964332026-03-15T07:36:57+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-lets-calculate-120x--80y--165-53459782026-04-24T15:56:32+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-for-now-ill-assume-the-required-protein-is-160g-but-its-not-61505542026-04-24T15:56:32+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-is-there-a-multiple-between-no-61134002026-04-24T15:57:06+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-in-the-solution-we-must-be-precise-14534872026-04-24T15:57:06+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-fibonacci-decomposition-with-distinct-terms-try-again-48405522026-04-22T17:59:26+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-can-we-use-5--3--2--1--1--1-no--invalid-due-to-duplicates-80333442026-04-22T17:59:26+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-can-a-group-have-size-1-yes-according-to-the-problem-35751892026-04-22T17:59:26+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-is-each-group-follows-the-fibonacci-sequence-interpreted-as-the-number-size-being-fibonacci-yes-20358062026-04-24T15:57:05+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-lets-confirm-following-the-fibonacci-sequence-likely-means-the-group-size-is-a-fibonacci-number--not-that-the-number-appears-somewhere-in-the-sequence-but-that-its-part-of-it-13131562026-04-24T15:57:05+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-earlier-thought-could-3-be-used-no-fewer-groups-74489012026-04-24T15:57:05+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-intuitively-after-how-many-weeks-suggests-positive-time-22430562026-04-22T18:00:26+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-lets-check-if-the-problem-means-after-how-many-full-weeks-from-the-start-will-it-exceed-since-it-starts-above-answer-is-0-81453362026-04-22T18:00:21+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-if-the-problem-intends-unique-pairs-data-is-insufficient-given-context-total-interaction-mentions-are-summed-76201002026-04-24T15:57:19+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-each-score-is-fixed-one-student-has-82-the-sixth-has-x-unknown-2756302026-04-24T15:57:39+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-its-given-as-82--contradiction-79754162026-04-22T18:00:39+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-biologically-flux-is-cumulative-however-for-modeling-often-final-amount-is-reported-48433462026-04-22T18:01:36+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-given-focal-spot-200-m-beyond-center--total-50--200--250-m-from-entry-center-78548392026-04-22T18:01:37+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-if-the-dome-is-transparent-and-curved-then-rays-that-go-deeper-diverge-due-to-curvature-2403812026-04-22T18:01:37+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-dome-radius-is-only-50-m--this-suggests-the-dome-is-the-lens-radius-50-m-meaning-the-surface-curves-from-center-outward-67493792026-04-22T18:01:37+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-if-the-surface-is-curved-then-rays-not-parallel-26255002026-04-22T18:01:37+00:00daily0.8https://docs.decisionpoint.org/spotlight/but--x---3--is-not-in-this-interval-so-no-solution-here-43873362026-04-22T18:04:14+00:00daily0.8https://docs.decisionpoint.org/spotlight/but--x--7--is-not-in--x--7--so-no-solution-here-89732122026-04-24T15:58:04+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-better-interpreted-its-a-permutation-of-8-people-taken-4-at-a-time-96323592026-04-24T15:58:31+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-answer-expected-is-a-number-based-on-production-2065792026-04-22T18:06:35+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-crew-needs-51-so-not-sufficient--but-the-total-generated-is-192-kg-24946362026-04-22T18:06:34+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-again-net-produced--if-interpreted-as-total-output-generated-by-all-systems-then-228-kg-80981482026-04-22T18:06:35+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-again-this-leads-to-no-solution-89848012026-04-24T15:59:31+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-check-bd-no--instead-use-full-geometry-minimize-abc--cd--da-22999782026-04-24T16:00:55+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-is-there-a-shorter-path-if-d-is-placed-differently-8638062026-04-24T16:00:55+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-instead-factor-by-grouping-or-use-synthetic-division-30607912026-04-24T16:03:04+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-better-recall-earlier-expression-7664902026-04-22T18:25:26+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-compute-numerically-for-simplicity-or-find-exact-fraction-40636682026-04-22T18:25:26+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-1918--1960-invalid-instead-the-new-discovery-is-after-1964-88687912026-04-22T18:26:05+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-1918-is-before-1960--not-possible-18183162026-04-22T18:26:05+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-initial-average-was-2133-now-much-smaller-that-only-happens-if-the-new-event-is-very-close-to-prior-ones-but-the-dominant-gaps-are-still-47-and-13-6893002026-04-22T18:26:10+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-1918-is-earlier-than-1947-so-if-its-a-discovery-in-the-past-it-would-have-been-included-so-it-cant-be-a-new-discovery-53050012026-04-22T18:26:10+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-1914-is-between-1900-and-1947--so-it-would-have-been-discovered-earlier-so-it-cant-be-a-new-discovery-40132142026-04-22T18:26:10+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-again-selecting-from-4-years-can-only-include-4-domains-43338602026-04-22T18:27:57+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-year-2-and-year-4-are-two-specific-years-among-five-and-selecting-4-years-from-5-means-omitting-one-to-exclude-year-2-must-omit-year-2-and-include-the-other-four-similarly-for-year-4-94117422026-04-22T18:27:57+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-year-1-and-year-3-are-both-included-in-all-selections-since-selecting-4-of-5-years-but-an-arbitrary-selection-might-miss-year-1-or-year-3-4934512026-04-22T18:27:57+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-given-the-structure-comparing-both-sides-68295832026-04-24T16:04:08+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-if-the-identity-is-meant-to-hold-for-specific--a--not-all-then-equating-90496572026-04-22T18:28:47+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-if-the-equation-is-valid-for-some--a--and-we-are-to-find--b--that-makes-it-valid-but-it-holds-only-when--a--0--again-89378122026-04-24T16:04:08+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-if--b--0--then--a--b--a---b--and-the-original-expression-is-undefined-when--a--b--but-here--b--0--so--a-16464512026-04-22T18:29:39+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-better-numerically-or-by-algebraic-max-29697302026-04-24T16:05:02+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-5089--5089-check-factoring-perhaps-error-70400862026-04-22T18:34:40+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-as-per-instruction-generate-valid-problem-87690732026-04-22T18:34:36+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-check-for-exact-solution-1885-is-not-a-perfect-square-but-since-time-must-be-positive-6784772026-04-22T18:38:44+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-instead-of-complex-algebra-consider-substituting--w--z--37441992026-04-22T18:41:03+00:00daily0.8https://docs.decisionpoint.org/spotlight/busy-professionals-swear-by-this-mail-merge-tricksee-how-instantly-33967992026-04-22T18:44:12+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-in-context-perhaps-accept-rounding-or-mistake-229892026-03-15T08:24:11+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-lets-assume-the-numbers-are-correct-and-find-closest-82801222026-03-15T08:24:11+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-for-consistency-with-format-and-since-problem-must-have-solution-reconsider-46597362026-03-15T08:24:11+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-in-math-olympiad-problems-have-integer-solutions-60685212026-03-15T08:24:11+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-in-educational-setting-sometimes-accept-the-expression-57415482026-03-15T08:24:12+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-for-magnitude-minimization-the-minimizing-k----67795542026-04-22T18:47:54+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-cross-product-zero-only-if-parallel-which-would-require-90566392026-04-22T18:55:40+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-in-educational-context-math-problems-may-allow-decimal-if-derived-but-final-answer-must-be-whole-30891612026-04-22T18:56:08+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-for-the-sake-of-the-problem-we-proceed-with-the-arithmetic-as-written-and-report-the-exact-result-as-362-but-not-acceptable-71456972026-03-15T08:35:39+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-in-math-problems-for-high-school-sometimes-they-accept-the-expression-but-here-final-answer-is-expected-to-be-boxed-1797412026-03-15T08:35:40+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-for-consistency-with-format-and-since-other-problems-use-exact-arithmetic-we-proceed-with-the-sum-59583862026-03-15T08:35:43+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-for-a-right-triangle-there-is-a-known-formula-35568582026-04-22T18:56:45+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-in-context-some-options-describe-outputs-however-function--action-so-only-a-is-a-definite-action-53794212026-04-22T19:03:19+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-e-says-synthesize-proteinswrong-47108162026-04-22T19:03:19+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-computed-total-mass-is-6660-kg-only-if-those-weights-are-exact-49250192026-04-24T16:12:10+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-expected-total-with-given-averages-is-24000-so-the-average-of-0555-kg-implies-6660-kg--contradiction-4040012026-04-24T16:12:15+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-data-mentions-2-kg--contradiction-14660022026-04-24T16:12:15+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-instruction-generate-a-clean-problem-92169732026-04-24T16:12:15+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-also-for-a-right-triangle-the-inradius-can-be-expressed-as-74745842026-04-22T19:09:47+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-2250-days-seems-long--617-years-unrealistic-for-aquifers-29508242026-04-22T19:11:14+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-in-the-new-list-the-three-values-that-come-after-15-are-likely-between-15-and-18-80405522026-03-15T08:51:06+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-if-original-has-a-value-16-say-20-but-median-still-15-1393272026-03-15T08:51:08+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-earlier-attempts-show-median-may-not-change-to-16-easily-4728882026-03-15T08:51:08+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-lets-look-for-a-different-approach-71393112026-03-15T08:51:08+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-in-the-context-and-since-no-specific-values-and-the-value-18-is-added-likely-only-one-value-falls-in-1516-but-not-necessarily-68359952026-03-15T08:51:10+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-better-the-median-is-25-unless-all-values-are--25--or-all--25--or-without-25-but-one-below-and-one-above-but-no-25--no-median-can-still-be-25-only-if-25-is-the-middle-62282722026-04-22T19:17:12+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-are-there-more-no--only-one-such-combination-19941292026-04-24T16:14:26+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-lets-compute-the-distance-to-the-nearest-point-on-the-rectangle-48796612026-04-24T16:15:32+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-15-cm-is-half-of-3-cm-which-is-the-smaller-dimension--correct-33593912026-04-24T16:15:32+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-lets-double-check-units-and-logic-27798212026-04-22T19:23:07+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-lets-re-express-in-precise-terms-20775512026-04-22T19:23:08+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-inscribed-usually-means-the-rectangles-vertices-lie-on-the-circle-65184222026-04-22T19:23:06+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-earlier-steps-had-error-in-assuming-radius-25-but-3-4-5-fits-in-25-cm-circle--correct-17247462026-04-22T19:23:12+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-in-context-use-exact-computation-31663822026-04-24T16:15:47+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-it-says-pollinate-but-not-collect-pollen--impossible-if-collecting-is-defined-22644062026-03-15T09:02:40+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-in-advanced-problems-sometimes-answer-is-irrational-52777792026-04-22T19:31:20+00:00daily0.8https://docs.decisionpoint.org/spotlight/but--x--35--2--so-this-intersection-is-outside-the-plot-instead-intersect-each-line-with--x--2--67722102026-04-22T19:33:35+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-for-box-use-exact-time-in-hours-or-minutes-stick-to-minutes-after-start-64320212026-04-22T19:36:26+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-for-simplicity-use-123730-or-better-use-minutes-past-900-93721102026-04-22T19:36:26+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-answer-format-expects-number-no--previous-examples-use-numbers-66884042026-04-22T19:36:26+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-final-answer-in-box--use-time-in-hours-or-round-42606532026-04-22T19:36:26+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-for-box-use-123730--not-numeric-44456512026-04-22T19:36:26+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-better-the-question-is-solved-and-the-answer-is-a-time--but-in-math-problems-sometimes-time-is-reported-in-hours-11310382026-04-24T16:18:26+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-in-context-use-the-exact-time-in-hours-18855272026-04-24T16:18:26+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-for-box-use-1238-rounded--too-approximate-76104392026-04-24T16:18:26+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-in-math-olympiad-fractional-minutes-are-acceptable-23289392026-04-24T16:18:24+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-900-am-is-540-minutes-so-total-855625-minutes-after-start-no--900-is-540-then-1h--610-70--680-11875--79875-minutes-after-900-61505042026-04-22T19:36:37+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-80-of-28-is-not-integer--so-maybe-typo-wait--perhaps-the-total-is-25-no-24--4--28-5317452026-04-22T19:37:16+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-in-context-of-olympiad-likely-80-is-meant-to-be-exact-so-maybe-total-after-is-not-28-but-24--4--28-70479382026-04-22T19:37:16+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-in-math-olympiads-sometimes-such-inconsistencies-are-avoided-10556992026-03-15T09:16:18+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-in-some-contexts-fractional-documents-dont-exist-so-perhaps-the-problem-has-a-typo-but-for-the-sake-of-generating-a-valid-olympiad-problem-lets-adjust-to-make-it-work-32591212026-03-15T09:16:18+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-in-the-original-we-said-4-more--so-to-keep-4-adjust-final-percentage-53920692026-03-15T09:16:19+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-for-the-sake-of-the-task-well-use-a-corrected-version-with-consistent-numbers-93330332026-03-15T09:16:20+00:00daily0.8https://docs.decisionpoint.org/spotlight/business-growth-starts-here-how-a-top-hcm-system-can-revolutionize-your-team-management-13746192026-04-22T19:39:11+00:00daily0.8https://docs.decisionpoint.org/spotlight/businesses-are-going-mainstreamheres-why-every-company-needs-human-capital-management-software-now-26767982026-04-22T19:39:11+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-at-n0-l20-10-and-it-increases-to-100-so-it-never-drops-below-10-contradiction-41711782026-04-22T19:41:58+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-instead-of-conjugates-factor-directly-62840332026-04-22T19:46:30+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-better-group-third-term-with-first-47952912026-04-22T19:46:30+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-in-5-second-increments-speed-is-95001922026-04-22T19:47:05+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-8333--10-so-within-first-interval-no--deeper-in-8402282026-04-22T19:47:05+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-in-competition-context-decimal-or-fraction-38425962026-04-22T19:47:05+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-in-context-number-of-people-must-be-integer-however-the-model-allows-fractional-interpretation-for-prediction-14457242026-04-24T16:22:13+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-in-math-competition-context-exact-fraction-may-be-accepted-but-here-answer-is-expected-numerical-86403002026-04-24T16:22:13+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-for-competition-they-may-expect-simplified-fraction-or-rounded-88438902026-04-24T16:22:14+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-in-context-we-report-the-exact-value-as-computed-70782812026-04-24T16:22:14+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-for-consistency-with-format-box-the-exact-decimal-from-calculation-46974792026-04-24T16:22:14+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-in-the-solution-steps-they-use-intermediate-calculations-93821072026-04-24T16:22:14+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-lets-assume-the-answer-is-to-be-reported-as-the-exact-decimal-from-calculation-even-if-not-integer-57775392026-04-24T16:22:14+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-in-the-context-people--perhaps-floor-no-3798542026-04-24T16:22:14+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-in-the-format-they-use--for-computation-then--with-number-70556922026-04-24T16:22:13+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-in-math-competitions-non-integer-answers-are-rare-for-countable-items-56545802026-04-24T16:22:14+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-lets-check-in-the-first-example-they-have-money-and-round-to-nearest-cent-so-decimal-is-ok-39657372026-04-22T19:52:10+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-lets-change-the-total-to-a-number-that-divides-evenly-but-we-cant-90144632026-04-22T19:52:10+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-for-decimal-use-417-but-lets-use-precise-fraction-or-decimal-90723442026-04-24T16:22:34+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-for-boxed-answer-use--417-but-others-are-exact-19615792026-04-24T16:22:34+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-for-the-sake-of-consistency-with-format-and-since-other-answers-are-exact-perhaps-the-problem-has-integer-answer-74064712026-04-24T16:22:34+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-lets-check-if-theres-a-better-way-33719602026-03-15T09:34:03+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-in-math-context-perhaps-keep-as-fraction-but-format-doesnt-32072752026-03-15T09:34:05+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-in-the-first-generated-they-have-11-so-fractional-is-fine-39543962026-04-24T16:22:54+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-lets-do-it-as-fraction-in-the-steps-and-decimal-in-answer-33860862026-04-24T16:22:54+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-given-the-context-and-that--bn--are-defined-explicitly-the-sum-is-35616462026-04-22T20:00:58+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-for-olympiad-likely-expects-numerical-evaluation-or-simplified-form-however-given-complexity-and-that-no-further-simplification-is-evident-the-sum-is-best-left-as-computed-numerically-but-we-round-to-reasonable-precision-41304322026-04-22T20:00:58+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-initial-mass-is-5-mg--seems-scaling-issue-44223712026-04-22T20:02:12+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-given-the-context-of-a-math-olympiad-and-numerical-precision-we-compute-64926432026-04-24T16:25:14+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-59-is-large-wait--perhaps-miscalculation-57346522026-03-15T09:49:52+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-210--210-sum-59--no-integer-solution-but-that-cant-be-76081952026-03-15T09:49:52+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-59-is-much-larger-than-maximum-possible-sum--contradiction-44499332026-03-15T09:49:52+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-for-exactness-keep-fractional-form-31666132026-03-15T09:50:49+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-in-math-olympiad-exact-fraction-is-preferred-61722172026-04-24T16:26:45+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-in-olympiad-fractional-is-fine-1239932026-04-22T20:11:32+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-lets-check-signs--all-consistent-26876752026-04-22T20:11:29+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-in-context-perhaps-its-better-to-leave-as-decimal-if-whole-but-its-not-84121482026-04-22T20:11:32+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-lets-do-it-as-decimal-for-alignment-with-samples-no--samples-use-exact-values-42187692026-04-22T20:11:29+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-lets-instead-generate-a-different-one-with-integer-answer-to-match-style-43907612026-04-22T20:11:29+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-falsifiability-applies-to-claims-not-observations-99346192026-04-22T20:18:25+00:00daily0.8https://docs.decisionpoint.org/spotlight/business-in-crisis-walgreens-being-forced-out-of-storesanalysis-you-cant-ignore-47428212026-04-22T20:32:37+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-health-index-cannot-be-negative--this-suggests-model-limitations-however-mathematically-95883752026-04-24T16:31:20+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-area-cannot-be-negativethis-implies-a-mathematical-model-not-physical-reality-the-function--lu--is-defined-mathematically-so-we-compute-algebraically-21385012026-04-22T20:41:15+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-in-many-such-problems-if-not-specified-proportional-with-angle-means-62799542026-04-22T20:47:29+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-here-the-only-choice-consistent-with-olympiad-style-is-to-compute-a-clean-number-38497342026-04-22T20:47:29+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-waitjoby-aviation-stock-price-jumps-300-is-this-the-big-break-47849152026-04-24T16:38:21+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-better-since-question-likely-expects-all-solutions-and-format-allows-descriptive-box-we-write-40298522026-04-22T21:10:40+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-will-you-save-huge-money-check-karls-mortgage-calculator-today-42663272026-04-22T21:12:10+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-as-per-instruction-pick-one-form-57304622026-03-15T10:52:36+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-lets-assume-it-wants-the-expression-16566632026-03-15T10:52:36+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-check-is-157-common-no-so-simplified-19969442026-04-22T21:17:08+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-deforestation-still-adds-10-ppm-total--but-only-if-its-proportional-71077132026-04-22T21:18:10+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-100-are-false-positives-due-to-population-stratification-so-these-are-not-true-99053632026-04-22T21:18:10+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-220-is-close-to-210-so-problem-may-have-typo-11839932026-04-22T21:28:23+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-in-context-likely-intended-solution-96095782026-04-22T21:28:24+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-better-perhaps-the-sum-is-186-but-given-210-73716252026-04-22T21:28:23+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-for-the-sake-of-the-format-assume-a-typo-and-use-a-solvable-version-89272132026-04-22T21:28:23+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-given-210-and-no-exact-solution-so-this-question-is-flawed-191572026-04-22T21:28:24+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-in-high-level-sometimes-non-integer-but-sequence-length-must-be-integer-30308232026-04-22T21:28:23+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-lets-recalculate-with-correct-logic-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nclude-288-00432--so-decimals-allowed-58213482026-04-22T22:59:10+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-in-production-systems-often-to-three-decimals-74829272026-04-24T17:03:58+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-earlier-steps-had-exact-integers-lets-recompute-with-exact-fractions-58983152026-04-22T22:59:10+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-in-original-examples-no-rounding-unless-specified-but-288-is-exact-367362026-04-22T22:59:10+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-98304-is-closer-to-983-than-984-98304--983-when-rounded-to-two-decimals-42991382026-04-24T17:03:58+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-lets-finalize-all-with-two-decimals-where-needed-33133842026-04-22T22:59:10+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-in-output-format-one-question-per-line-then-answer-15045302026-04-22T22:59:11+00:00daily0.8https://docs.decisionpoint.org/spotlight/but--t--41--is-in-the-year-2004-since--t--0--is-2000-so-the-anomaly-first-exceeds-30-during-2004-but-the-official-year-is-2004-however-the-first-full-year-where-its-above-is-2005-but-the-model-is-continuous-typically-we-report-when-it-crosses-64246382026-04-24T17:04:45+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-lets-check--t--41--4---t--3045--30--so-the-event-occurs-at--t--41--which-is-in-2004-35024382026-04-24T17:04:44+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-earlier-calculation--t--4--gives--t--30--so-the-first-time-it-exceeds-is-just-after-2004-so-the-answer-is-2004-20357982026-04-24T17:04:45+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-lets-double-check-at--t--4---t--30--not-greater-at--t--41---t--3045--30--and--2000--41--20041--which-is-in-the-year-2004-83751742026-03-15T12:41:07+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-based-on-format-a-standard-problem-is-72142792026-04-24T17:06:16+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-better-to-check-if-this-matches-expected-form-12348262026-04-22T23:10:39+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-instead-use-known-identity-this-is-similar-to-hypergeometric-but-lets-accept-the-complexity-95017752026-04-22T23:10:42+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-7200-years-is-much-less--contradiction-57120192026-04-22T23:13:19+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-for-formal-math-context-with-correct-probability-2735622026-04-24T17:07:05+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-data-says-40-effective-with-both--contradiction-15262772026-03-15T13:05:56+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-it-says-40-effective--so-use-that-value-31091362026-03-15T13:05:58+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-youve-never-heard-of-this-minority-minority--heres-whats-inside-32505692026-04-22T23:32:38+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-in-math-problems-like-this-sum-of-geometric-series-a--40-r--115-n--5-62397982026-03-15T13:17:33+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-better-to-use-rounded-or-exact-the-sum-is-26969525-which-is-26969525-however-in-practice-you-cant-tag-a-fraction-but-the-mathematical-model-uses-continuous-approximation-since-this-is-a-modeling-problem-we-accept-the-decimal-68479162026-03-15T13:17:35+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-lets-avoid-scientific-notation-and-keep-six-decimals-as-in-prior-pattern-eg-9375-38518082026-03-15T13:17:33+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-for-consistency-with-format-and-avoid-unnatural-decimals-note-that-in-the-pie-problem-money-led-to-71-so-decimals-are-ok-69137132026-03-15T13:17:33+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-as-only-one-tambo-fixed-unless-placements-avoid-overlap-total-arc-needed-for-multiple-but-not-specified-74488902026-04-22T23:43:14+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-in-context-perhaps-expect-exact-expression-53697082026-04-22T23:52:22+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-in-real-context-rounding-not-done-however-educational-math-problems-use-exact-arithmetic-64051392026-04-22T23:52:43+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-all-prior-examples-use-integers-29719012026-04-22T23:52:52+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-in-academic-settings-such-problems-sometimes-use-exact-fractions-85267152026-04-22T23:52:45+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-in-the-context-of-the-problem-its-acceptable-to-report-the-mathematical-result-as-336-but-final-answers-in-examples-are-integers-37935022026-04-24T17:15:54+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-55-corresponds-to-3500-not-directly--adjusted-to-the-nearest-century-likely-means-round-the-numerical-value-3455-to-the-nearest-century-3500-58669552026-04-22T23:59:07+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-lets-compute-1724--1731--1724173134553455-3455-mod-100--34551005555-round-55-to-nearest-hundred-2004742026-04-22T23:59:07+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-is-a-higher-number-possible-try-480-2834262026-04-24T17:18:10+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-is-720-always-dividing-we-tested-several--yes-59000092026-04-24T17:18:10+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-in-context-maybe-typo--suppose-fourth-has-half-the-second-instead-but-not-14033772026-04-24T17:19:29+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-better-to-assume-typo--perhaps-fourth-has-half-the-second-instead-of-third-89759052026-04-24T17:19:29+00:00daily0.8https://docs.decisionpoint.org/spotlight/business-giants-ranked-top-multinational-corporations-you-need-to-know-before-they-rule-the-future-80312022026-03-15T13:45:21+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-04096-is-4096-but-we-report-numerical-value-68634032026-04-23T00:15:41+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-consider-suppose-we-set--x--y--then-undefined-so-domain-excludes--x--y--34615882026-04-23T00:21:38+00:00daily0.8https://docs.decisionpoint.org/spotlight/but--m--must-be-a-positive-integer-since-the-pattern-repeats-every-12-months-we-find-the-equivalent-positive-month-by-computing-modulo-12-however-the-grant-issuance-month-is-tied-to--m--which-must-be-in-the-range--1--to--12--the-general-solution-is-42336442026-04-23T00:35:46+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-if-second-term-is-3-and-sum-8-then-unless-complex-no-solution-86454122026-04-23T00:44:34+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-for-advanced-students-perhaps-complex-ratio-not-realistic-87405062026-04-23T00:44:34+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-check-30-off-250--175-minus-40--135-14028972026-04-24T17:30:55+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-if-only-one-is-listed-assume-same-63885952026-04-23T00:45:18+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-in-context-perhaps-intended-different-84539402026-04-24T17:30:56+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-daily-consumption-is-550-liters-so-one-reactor-produces-far-more-than-needed-62531992026-04-23T00:51:58+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-energy-is-5400-watt-hours-rate-is-450-w-43777202026-04-23T00:51:58+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-is-this-the-only-solution-lets-reconsider-42095142026-03-15T14:29:26+00:00daily0.8https://docs.decisionpoint.org/spotlight/but--y--0--makes--x---y--x---x--y--x--so-the-original-expression-is-10730932026-03-15T14:29:26+00:00daily0.8https://docs.decisionpoint.org/spotlight/busted-no-tax-on-overtime-means-big-savingsstart-claiming-today-before-its-gone-31869962026-04-23T00:57:23+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-clickbait-titles-should-reflect-scale-lets-reframe-using-correct-large-units-17927412026-04-23T01:06:02+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-for-clickbait-use-precise-value-50963532026-04-23T01:06:03+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-better-to-use-scientific-or-clearer-64814092026-04-23T01:06:03+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-for-clickbait-likely-expect-large-number-5204022026-04-23T01:06:03+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-lets-proceed-with-correct-science-and-scale-27280712026-04-23T01:06:03+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-due-to-periodicity-average-value-of-sine-and-cosine-over-full-periods-is-zero-89165072026-04-23T01:19:22+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-in-context-of-pharmacology-and-drug-spread-often-such-problems-imply-the-number-of-reachable-lattice-points-within-observable-range-however-the-key-insight-comes-from-parity-50441672026-04-23T01:21:58+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-in-the-absence-of-bounds-the-only-finite-answer-from-parity-is-pattern-9698182026-04-23T01:21:59+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-lets-look-for-a-finite-meaningful-interpretation-78644772026-04-23T01:21:59+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-lets-reconsider-total-number-of-positions-is-7-91171202026-04-23T01:25:44+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-actually-is-the-block-method-valid-yes-and-its-simpler-number-of-favorable--150-total--210-so-7486212026-04-23T01:25:44+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-best-to-leave-compressed-or-verify-57493842026-04-24T17:42:47+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-based-on-format-likely-expects-calculate-z-for-final-exam-71110392026-03-15T15:04:14+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-is-this-the-only-constraint-yes--the-equation-5p---6q---1-has-infinitely-many-solutions-but-the-problem-states-there-exist-constants--implying-one-such-pair-is-acceptable-and-in-olympiad-problems-like-this-often-the-solution-is-unique-under-minimal-assumptions-or-integer-requirement-given-the-context-11-is-a-valid-predictable-solution-68126882026-04-24T17:44:49+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-each-pair-consists-of-one-a-and-one-u--so-number-of-a-u-pairs-as-interactions-is-300-total-1200-nucleotide-positions-belong-to-pairs--so-300-out-of-1200-pairs-are-a-u-57298142026-04-23T01:36:15+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-if-density-decreases-increase-is-negative-however-likely-the-question-intends-if-same-number-per-unit-area-but-area-increases-but-public-parks-grow-from-10km-to-14km-radius--use-area-ratio-63382902026-04-23T01:37:01+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-by-how-many-times-often-means-ratio-20167362026-04-23T01:37:01+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-given-density-decreases-contradiction-92578322026-04-23T01:37:01+00:00daily0.8https://docs.decisionpoint.org/spotlight/business-download-gone-viral-unlock-onedrives-hidden-power-now-56137872026-04-24T17:46:07+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-in-olympiad-problems-such-answers-are-not-typical-likely-a-misinterpretation-68173982026-04-24T17:46:25+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-for-the-sake-of-the-task-assume-the-problem-is-correct-and-use-exact-computation-1055692026-04-23T01:41:12+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-210-is-between-185-and-220-and-none-integer-recheck-discriminant-85285282026-04-24T17:47:01+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-210-cannot-be-achieved-for-integer-n-66527352026-04-24T17:47:04+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-for-surface-or-area-we-need-exact-86269722026-04-24T17:47:01+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-in-context-perhaps-the-problem-allows-decimal-no--n-integer-4860542026-04-24T17:47:04+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-for-exercise-use-approximate-solution-or-reconsider-44971822026-04-24T17:47:01+00:00daily0.8https://docs.decisionpoint.org/spotlight/business-owners-are-obsessed-how-opsmerchant-transformed-their-operations-94552782026-04-24T17:50:40+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-in-context-population-must-be-integer--so-round-to-nearest-or-assume-continuous-approximation-99475612026-03-15T15:34:11+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-in-such-problems-unless-specified-use-the-exact-value-however-the-format-of-previous-answers-suggests-integer-but-1991-is-closer-49683292026-03-15T15:34:12+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-in-math-olympiad-sometimes-fractional-populations-are-accepted-in-transient-models-28505582026-03-15T15:34:13+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-in-context-the-expected-answer-is-likely-1991-if-rounded-or-perhaps-the-problem-allows-decimal-21650852026-03-15T15:34:17+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-in-math-olympiad-sometimes-exact-fractional-answer-but-format-uses-integers-61181522026-03-15T15:34:14+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-in-the-initial-problems-even-with-percentages-answers-were-exact-38130762026-03-15T15:34:15+00:00daily0.8https://docs.decisionpoint.org/spotlight/business-insiders-reveal-hidden-profits-master-every-options-chain-like-a-pro-97964272026-03-15T15:34:16+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-is-that-the-only-one-yes--only-one-way-to-choose-all-five-digits-and-arrange-in-increasing-order-94252062026-04-23T01:59:20+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-is-there-a-5-digit-increasing-number-like-12345--yes-72258692026-04-23T01:59:19+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-is-there-a-number-like-12435-no--not-increasing-80303202026-04-23T01:59:21+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-is-there-12435-no--not-increasing-66518562026-04-23T01:59:20+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-lets-confirm-with-a-combinatorial-approach-52528952026-04-23T01:59:22+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-is-there-a-possibility-of-using-fewer-digits-no--must-be-5-digit-strictly-increasing--so-5-distinct-digits-14331772026-04-23T01:59:26+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-in-a-strictly-increasing-sequence-the-first-digit-must-be-the-smallest-so-if-0-is-in-the-set-it-must-be-first-making-the-number-invalid-49831482026-04-23T01:59:26+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-isolating-means-they-stop-transmitting-the-next-day-30373182026-04-23T02:01:53+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-3125--200-and-it-stabilizes-so-it-remains-above-14462982026-04-23T02:01:51+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-for-the-sake-of-mathematical-consistency-assume-we-find-when-it-first-goes-below-200--but-it-doesnt-40061312026-04-23T02:01:51+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-from-model-v-approaches-3125-from-below-no--starts-at-300-goes-to-2995-then-3012-so-increases-slightly-stabilizes-67919322026-04-23T02:01:54+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-better-go-back-to-the-vector-equation-92664092026-04-23T02:03:23+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-lets-compute-the-numerical-value-accurately-53874122026-04-23T02:05:50+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-all-gpus-run-simultaneously-so-total-time--32-hours-parallelized-across-5-gpus-72610782026-04-24T17:55:30+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-assume-problem-expects-integer--perhaps-typo-83139672026-03-15T15:51:18+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-in-context-perhaps-the-intended-answer-is-n--10-but-sum-is-185-29860642026-03-15T15:51:20+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-for-realism-assume-the-problem-meant-66142792026-03-15T15:51:21+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-in-high-level-problems-sometimes-the-answer-is-approximate-but-not-for-olympiad-47555892026-03-15T15:51:22+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-for-the-purpose-of-the-exercise-and-assuming-a-possible-typo-in-the-problem-suppose-the-intended-function-allowed-a-zero-derivative-however-as-written-no-finite-solution-66514332026-04-23T02:16:18+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-for-the-task-we-output-the-5-titles-as-requested-first-then-the-answer-53129262026-04-23T02:16:17+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-for-simplicity-and-correctness-use-direct-substitution-and-collect-terms-42521662026-03-15T15:59:54+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-in-low-terms-after-careful-expansion-standard-in-such-recursive-functional-iterations-the-final-expression-simplifies-to-50277582026-03-15T15:59:54+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-each-topic-type-is-used-exactly-once-cannot-hold-if-total-categories-sum-to-9-and-only-7-days-60691502026-04-23T02:24:50+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-priestleys-style-suggests-a-finite-answer-re-examining-perhaps-the-expression-is-bounded-62008112026-04-23T02:26:05+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-intuitively-load-balancing-allows-fewer-servers--but-cost-model-is-per-server-hour-so-if-we-run-fewer-cost-drops-62296952026-04-24T18:00:14+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-at-080-per-server-hour-that-would-be-misleading-57400812026-04-23T02:30:07+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-is-this-correct-the-problem-says-only-75-of-servers-are-needed-on-average--so-average-consumption-is-75-of-full-capacity-but-the-pricing-model-charges-per-server-used--but-if-a-server-is-idle-25-of-time-but-charged-at-080-per-hour-regardless-that-doesnt-reflect-usage-10078442026-04-24T18:00:15+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-is-181-bce-correct-356---100--256-256---50--206-206---25--181-yes-30497812026-04-23T02:30:07+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-in-context-must-be-whole-maybe-the-percentage-is-exact-so-we-proceed-numerically-or-assume-rounding-26511132026-04-23T02:30:07+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-in-real-contexts-percentages-of-discrete-items-must-yield-integers-85927882026-04-23T02:30:06+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-ai-utility-patents-must-be-whole-16764882026-04-23T02:30:05+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-lets-calculate-exactly-with-fractions-87038752026-04-24T18:00:15+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-a-better-method-compute-the-intersection-by-analyzing-the-boundaries-49460922026-03-15T16:07:13+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-is-the-region-symmetric-yes-because-replacing-y-with--y-preserves-both-inequalities-9563242026-03-15T16:07:16+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-based-on-algebra-no-non-zero-common-solution-60131412026-04-24T18:00:45+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-in-video-they-might-say-it-returns-visually-52706452026-04-24T18:00:44+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-lets-assume-the-net-decrease-is-12-so-92864482026-04-23T02:31:50+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-final-answer-should-be-integer-wait--12-of-45000-7511892026-04-23T02:40:55+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-in-multiple-choice-or-box-we-write-432-but-previous-answers-are-integers-57371422026-04-23T02:41:09+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-in-context-likely-expect-exact-value-21066152026-04-23T02:41:05+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-in-all-prior-examples-answers-are-integers-1861322026-04-23T02:41:08+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-in-real-systems-its-the-expected-number-so-we-report-432-28968332026-04-23T02:41:08+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-in-the-context-maybe-they-expect-4-but-thats-not-accurate-56908482026-04-23T02:41:08+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-lets-change-the-approach-perhaps-the-12-is-approximate-but-no--we-take-it-as-exact-525992026-04-23T02:41:08+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-in-the-initial-instruction-all-answers-are-integers-so-lets-adjust-the-solution-to-reflect-a-realistic-scenario-where-the-number-is-integer-11659482026-04-23T02:41:09+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-better-to-have-an-integer-answer-23204382026-04-23T02:41:10+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-lets-move-to-a-different-one-to-avoid-issue-30267132026-04-23T02:41:10+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-in-the-initial-examples-all-are-integers-so-ill-adjust-the-problem-to-make-it-integer-69660612026-04-23T02:41:10+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-in-context-maybe--u--is-a-positive-number-but-not-unique-74762152026-04-23T02:43:50+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-in-olympiad-problems-such-equivalence-usually-means-the-equation-is-identically-satisfied--so-any--u--is-acceptable-but-if-we-assume-a-specific-value-is-expected-perhaps-a-misstep-42167042026-04-23T02:43:51+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-in-the-absence-of-additional-constraints-the-equation-is-identically-satisfied-however-for-olympiad-problems-often-such-questions-have-unique-answers--so-perhaps-reconsider-the-setup-48963122026-04-23T02:43:51+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-as-per-instruction-generate-a-valid-question-with-solution-74774102026-04-23T02:43:51+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-for-consistency-with-format-and-since-the-calculation-is-correct-the-solution-is-all-real-numbers--but-we-cant-box-that-43864152026-04-23T02:43:50+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-for-the-sake-of-completion-and-as-a-math-olympiad-may-expect-recognition-but-here-perhaps-the-intended-answer-is-derived-from-a-different-setup-92816432026-04-23T02:43:51+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-in-the-context-of-the-journalist-storytelling-perhaps-they-measured-and-averaged-and-found-it-equals--4u2--and-want-to-find--u---but-mathematically-its-always-true-3268382026-04-24T18:04:33+00:00daily0.8https://docs.decisionpoint.org/spotlight/busy--out-of-office-these-mic-pro-tips-will-make-your-status-game-stronger-93263832026-04-23T02:45:07+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-covering-a-disk-with-identical-non-overlapping-circles-interiors-disjoint-to-cover-the-whole-disk-is-impossible-unless-the-small-circles-fill-space-efficiently--which-they-dont-due-to-gaps-51664302026-04-24T18:05:07+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-a-more-precise-and-realistic-olympiad-level-interpretation-5337782026-04-24T18:05:05+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-is-625-considered-to-end-in-0625-the-last-four-digits-of-625-are-0625--yes-it-is-0625-when-padded-to-four-digits-28900852026-04-24T18:06:18+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-is-0625-the-last-four-digits-yes--625-is-0625-when-written-with-leading-zeros-in-mathematics-this-is-standard-34322032026-04-24T18:06:33+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-earlier-we-thought-15--but-5-is-smaller-and-works-69755662026-04-24T18:06:32+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-in-standard-interpretation-the-last-four-digits-of-625-are-0625--yes-because-625-is-written-as-0625-64900102026-04-24T18:06:37+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-earlier-we-missed-this--the-solution-is-lighter-42562502026-04-24T18:06:37+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-instruction-says-generate-5-clickbait-seo-friendly-titles-and-conclusion-with-boxed-final-answer-14325582026-04-24T18:06:37+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-is-7-the-first-what-about--t1--not-a-multiple-of-7--t23456--none-are-multiples-of-7-first-multiple-of-7-is-7-73589942026-04-23T02:51:35+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-actually-we-want-first--n--where-quantum-time-is-strictly-less--which-is--n--1--38961622026-03-15T16:32:20+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-are-the-others-repeated-no--all-fractions-are-distinct-14958102026-04-23T03:05:04+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-for-total-data-compute-sum-over-all-particles-24394092026-04-23T03:09:03+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-is-colony-doubling-day-10-a-production-trigger-the-problem-says-starti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but-if-we-consider-the-algebraic-simplification-before-substitution-we-had-41934542026-04-23T04:38:22+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-if-we-are-to-report-a-finite-value-under-the-assumption-that-the-original-equation-holds-the-only-possibility-is--y--0--and-the-expression-becomes-42544562026-04-23T04:38:22+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-due-to-packing-and-disjointness-constraints-we-cannot-achieve-this-67822602026-04-24T18:39:13+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-due-to-the-disjointness-centers-must-be-at-least-2-meters-apart-89085022026-04-24T18:39:14+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-instead-using-standard-simplification-from-geometric-identities-36954172026-04-24T18:41:50+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-after-verification-the-correct-and-simplified-known-ratio-is-51111302026-04-23T04:52:28+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-after-consulting-known-problems-the-intended-answer-is-often-67954332026-04-23T04:52:28+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-in-standard-olympiad-solutions-the-ratio-is-often-simplified-to-a-boxed-expression-68537292026-04-23T04:52:28+00:00daily0.8https://docs.decisionpoint.org/spotlight/but--fa--b--c--fa--fb--fc--so-14484042026-04-23T05:04:03+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-in-the-sample-problems-answers-are-unique-57222502026-04-23T05:05:51+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-better-lets-recompute--is-there-a-standard-way-no-but-perhaps-the-problem-has-a-typo-or-perhaps-we-are-to-find-the-magnitude-36688342026-04-23T05:05:50+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-whats-hiding-behind-the-rockstar-gaming-stock-surge-expert-analysis-inside-53098692026-03-15T18:45:05+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-in-real-world-it-would-be-rounded-for-math-problem-assume-exact-computation-and-round-final-answer-77241262026-03-15T18:51:32+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-105-is-exactly-halfway--in-many-contexts-rounds-to-11-21613172026-03-15T18:51:32+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-195-is-odd-so-half-is-975--impossible-31249672026-03-15T18:51:33+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-for-correctness-and-since-the-angle-may-be-a-narrative-device-we-output-solutions-12075302026-04-23T05:28:14+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-better-to-write-as-reduced-fraction-verify-27304772026-04-24T18:52:00+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-in-this-case-16-and-17-are-close-so-near-uniform-93308462026-04-24T18:52:00+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-lets-correct-the-earlier-mistake-the-class-sizes-are-not-symmetric-so-we-cannot-use-binomial-symmetry-but-our-enumeration-is-exact-58217002026-04-24T18:51:59+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-for-exact-calculation-with-full-precision-83007722026-04-23T05:37:51+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-context-user-count-can-be-modeled-continuously-however-standard-is-to-round-to-nearest-integer-76508432026-04-23T05:37:52+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-4525-is-exactly-halfway--convention-rounds-up-65371702026-04-23T05:37:52+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-in-educational-contexts-sometimes-kept-fractional-26259422026-04-23T05:37:52+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-4525-is-not-exactly-halfway-4525-is-exactly-halfway-between-452-and-453-96276012026-04-23T05:37:52+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-cell-count-should-be-integer-so-round-down-at-end-79365882026-04-23T05:37:52+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-among-the-consonants-there-are-duplicates-n-3-g-2-r-1-the-vowel-block-is-treated-as-one-unit-29656132026-04-23T05:39:32+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-youve-been-missing-the-school-status-what-this-means-for-students--parents-35275452026-04-23T05:39:49+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-in-olympiad-problems-such-trick-questions-exist-however-for-consistency-perhaps-the-intended-number-is--2025--but-it-says-2024-98919902026-04-24T18:54:13+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-as-written-no-such--n--however-for-the-sake-of-a-constructive-problem-suppose-the-ending-was--0000--but-not-helpful-72747282026-04-24T18:54:12+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-2025-is-odd-so--n--must-be-odd-77105542026-04-24T18:54:12+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-1600-is-the-only-perfect-square-in-the-ballpark-and-historically-closer-88067342026-03-15T19:21:49+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-it-also-says-operational-time-this-month-is-15-times-longer-however-per-day-is-emphasized-suggesting-rate-context-23772102026-03-15T19:42:48+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-is-area-per-day-intrinsic-or-operational-the-increase-is-due-to-both-faster-data-collection-and-longer-time-so-57251842026-03-15T19:42:50+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-earlier-330-which-interpretation-22028152026-04-23T06:06:11+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-assuming-a-typo-and-suppose-it-is-critical-then-only-way-is-evaluate-sign-change-31121422026-03-15T19:42:54+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-are--10--and---10--generated-no-so-total-71095892026-04-23T06:08:37+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-compute--x5--362--100--so-stop-94795372026-04-23T06:08:37+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-for-olympiad-perhaps-they-expect-solving-the-quadratic-34151052026-04-23T06:10:56+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-440-is-given--maybe-its-a-trick-23416992026-04-23T06:10:57+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-for-integer-olympiad-likely-typo--but-to-proceed-perhaps-the-intended-answer-is-n--20-but-sum-is-420-21643462026-04-23T06:10:57+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-440-is-not-of-the-form-nn1-for-integer-n--65091292026-04-23T06:10:59+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-in-context-perhaps-the-problem-is-different-48450642026-04-23T06:11:00+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-from--dx--2a-x--a--b--and--d2024--1--we-need--d2025--2a2025--a--b--express-in-terms-of-knowns-39422552026-04-23T06:19:24+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-instead-manipulate-the-equation-algebraically-19266872026-04-23T06:20:55+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-youll-hate-how-smash-carts-madness-unfoldswatch-inside-2823312026-04-23T06:24:05+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-better-number-of-functions-multinomial-coefficient-94578352026-04-23T06:34:30+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-for-each-the-birds-are-assigned-to-fixed-zones-so-total-for--a1--56-15579952026-04-23T06:34:30+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-24-is-achieved-so-24-is-the-largest-such-integer-56043832026-04-23T06:37:40+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-in-context-accept-closest-however-re-solve-23285432026-03-15T20:17:30+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-for-sake-of-format-accept-approximate-61248772026-04-24T19:08:06+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-in-the-solution-show-steps-and-box-the-exact-solution-as-per-formula-even-if-not-integer-but-not-realistic-4134772026-04-24T19:08:08+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-instruction-is-to-generate-new-questions-so-i-can-design-a-solvable-one-90457562026-04-24T19:08:06+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-for-the-response-ill-use-a-different-question-96938392026-04-23T06:39:51+00:00daily0.8https://docs.decisionpoint.org/spotlight/busting-myths-download-any-song-on-soundcloud-without-falling-off-track-12710922026-04-24T19:08:22+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-waitthis-sql-case-syntax-trick-will-blow-your-queries-away-8831422026-04-23T06:53:48+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-for-the-purpose-of-this-task-and-since-the-format-requires-a-clean-answer-perhaps-the-intended-value-is-124-so-n8-91084332026-04-24T19:11:59+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-olympiad-problems-rarely-have-non-integer-answers-3180432026-04-24T19:11:59+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-based-on-phrasing-2-motion-related-m-v--this-means-m-and-v-are-distinct-so-total-items-all-6-are-distinct-the-mention-of-categories-is-descriptive-not-indicating-indistinguishability-however-the-instruction-says-assuming-datasets-of-same-type-are-indistinguishable-but-here-since-each-parameter-is-used-once-and-they-are-distinct-labels-they-are-distinguishable-12551412026-04-23T06:57:20+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-lets-assume-a-better-interpretation-perhaps-the-educator-records-the-value-type-and-within-a-type-values-are-indistinct--but-here-each-value-is-used-once-and-even-m-and-v-are-different-49643592026-04-23T06:57:20+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-lets-check-if-the-problem-says-indistinguishable-as-a-general-rule-but-here-they-are-not-75404592026-04-23T06:57:15+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-lets-look-for-similar-problems-in-combinatorics-if-you-have-labeled-items-permutations-are-full-factorial-88023772026-04-23T06:57:24+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-48-is-not-congruent-with-difficulty-46701682026-04-23T06:57:25+00:00daily0.8https://docs.decisionpoint.org/spotlight/but-lets-assume-the-biologist-records-a-2d-array--so-48-entr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