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instruction string | context string | response string | source string | text string |
|---|---|---|---|---|
Generate an executable Python function generated from the given prompt. The function should take stdin as input and print the output. Simply call the function after the definition.You are given a binary matrix A of size n × n. Let's denote an x-compression of the given matrix as a matrix B of size n/x × n/x such that f... | Expertise Code - Souveraineté Cygnis | [RÉFLEXION] Analyse approfondie de la problématique code.
Validation : Protocole de haute précision Simonc-44 activé.
[RÉPONSE]
<|begin_of_thought|>
Okay, let's see. The problem is to find the maximum x such that the given binary matrix can be x-compressed. An x-compression means that the matrix is divided into x by... | null | null |
Return your final response within \boxed{}. Michael writes down all the integers between 1 and \( N \) inclusive on a piece of paper and discovers that exactly \( 40\% \) of them have leftmost digit 1. Given that \( N > 2017 \), find the smallest possible value of \( N \). | Expertise Logic - Souveraineté Cygnis | [RÉFLEXION] Analyse approfondie de la problématique logic.
Validation : Protocole de haute précision Simonc-44 activé.
[RÉPONSE]
<|begin_of_thought|>
Okay, so Michael wrote down all the integers from 1 to N, and found that exactly 40% of them have a leftmost digit of 1. We need to find the smallest possible N that's... | null | null |
Generate an executable Python function generated from the given prompt. The function should take stdin as input and print the output. Simply call the function after the definition.Andrew and Jerry are playing a game with Harry as the scorekeeper. The game consists of three rounds. In each round, Andrew and Jerry draw r... | Expertise Code - Souveraineté Cygnis | [RÉFLEXION] Analyse approfondie de la problématique code.
Validation : Protocole de haute précision Simonc-44 activé.
[RÉPONSE]
<|begin_of_thought|>
Okay, let's see. So the problem is to find the probability that Jerry's sum of three balls is strictly higher than Andrew's, given that Andrew won the first two rounds ... | null | null |
Return your final response within \boxed{}.
Angle $\widehat{A}$ is the smallest in triangle $ABC$. Points $B$ and $C$ divide the circumcircle of the triangle into two arcs. Let $U$ be a point on the arc bounded by $B$ and $C$ that does not contain $A$.
The perpendicular bisectors of segments $[AB]$ and $[AC]$ interse... | Expertise Logic - Souveraineté Cygnis | [RÉFLEXION] Analyse approfondie de la problématique logic.
Validation : Protocole de haute précision Simonc-44 activé.
[RÉPONSE]
<|begin_of_thought|>
Okay, let's see. I have this geometry problem here. It says that in triangle ABC, angle A is the smallest. Points B and C divide the circumcircle into two arcs, and U ... | null | null |
"How does the hypothesis of dark matter consisting of dark atoms or dark molecules affect our curren(...TRUNCATED) | Expertise Science - Souveraineté Cygnis | "[RÉFLEXION] Analyse approfondie de la problématique science.\n\nValidation : Protocole de haute p(...TRUNCATED) | null | null |
"Return your final response within \\boxed{}. Given a circle \\( \\odot O \\), point \\( A \\) lies (...TRUNCATED) | Expertise Logic - Souveraineté Cygnis | "[RÉFLEXION] Analyse approfondie de la problématique logic.\n\nValidation : Protocole de haute pr(...TRUNCATED) | null | null |
"How can we use quantum chemistry methods to predict the electronic and magnetic properties of new m(...TRUNCATED) | Expertise Science - Souveraineté Cygnis | "[RÉFLEXION] Analyse approfondie de la problématique science.\n\nValidation : Protocole de haute p(...TRUNCATED) | null | null |
"Return your final response within \\boxed{}. Determine all the functions \\( f: \\mathbb{R} \\right(...TRUNCATED) | Expertise Math - Souveraineté Cygnis | "[RÉFLEXION] Analyse approfondie de la problématique math.\n\nValidation : Protocole de haute pré(...TRUNCATED) | null | null |
"Return your final response within \\boxed{}. On a plane, a point \\( O \\) is marked. Is it possibl(...TRUNCATED) | Expertise Logic - Souveraineté Cygnis | "[RÉFLEXION] Analyse approfondie de la problématique logic.\n\nValidation : Protocole de haute pr(...TRUNCATED) | null | null |
"Return your final response within \\boxed{}. Prove the following theorem: Let a triangle have side (...TRUNCATED) | Expertise Math - Souveraineté Cygnis | "[RÉFLEXION] Analyse approfondie de la problématique math.\n\nValidation : Protocole de haute pré(...TRUNCATED) | null | null |
End of preview.