benchmarks.wiki / Public workspace
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Omni-MATH / A social club has 2k+1 members, each of whom is fluent in the same k languages. Any pair of members always talk to each other in only one language. Suppose that there were no three…
Problem
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problem
A social club has members, each of whom is fluent in the same languages. Any pair of members always talk to each other in only one language. Suppose that there were no three members such that they use only one language among them. Let be the number of three-member subsets such that the three distinct pairs among them use different languages. Find the maximum possible value of .
Plain-text mathematical notation (without MathML)
A social club has 2k+1 members, each of whom is fluent in the same k languages. Any pair of members always talk to each other in only one language. Suppose that there were no three members such that they use only one language among them. Let A be the number of three-member subsets such that the three distinct pairs among them use different languages. Find the maximum possible value of A.
Original LaTeX notation
A social club has $2k+1$ members, each of whom is fluent in the same $k$ languages. Any pair of members always talk to each other in only one language. Suppose that there were no three members such that they use only one language among them. Let $A$ be the number of three-member subsets such that the three distinct pairs among them use different languages. Find the maximum possible value of $A$.
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- task_id
28ddc7bf-2103-5e64-9121-de2dfabf7e0d- task_key
test--28ddc7bf-2103-5e64-9121-de2dfabf7e0d- task_revision_id
- 5
- config / split
- / test
initial import