benchmarks.wiki / Public workspace
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Omni-MATH / At a conference there are n mathematicians. Each of them knows exactly k fellow mathematicians. Find the smallest value of k such that there are at least three mathematicians that …
Problem
Answer published by the source. Consult the official source to check your work against its answer.
problem
At a conference there are mathematicians. Each of them knows exactly fellow mathematicians. Find the smallest value of such that there are at least three mathematicians that are acquainted each with the other two.
[color=#BF0000]Rewording of the last line for clarification:[/color]
Find the smallest value of such that there (always) exists mathematicians such that and know each other, and know each other and and know each other.
Plain-text mathematical notation (without MathML)
At a conference there are n mathematicians. Each of them knows exactly k fellow mathematicians. Find the smallest value of k such that there are at least three mathematicians that are acquainted each with the other two. [color=#BF0000]Rewording of the last line for clarification:[/color] Find the smallest value of k such that there (always) exists 3 mathematicians X,Y,Z such that X and Y know each other, X and Z know each other and Y and Z know each other.
Original LaTeX notation
At a conference there are $n$ mathematicians. Each of them knows exactly $k$ fellow mathematicians. Find the smallest value of $k$ such that there are at least three mathematicians that are acquainted each with the other two. [color=#BF0000]Rewording of the last line for clarification:[/color] Find the smallest value of $k$ such that there (always) exists $3$ mathematicians $X,Y,Z$ such that $X$ and $Y$ know each other, $X$ and $Z$ know each other and $Y$ and $Z$ know each other.
Discussion
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Source and history
- task_id
bb5bbf05-7a13-5e3a-9d27-540c8c16dcca- task_key
test--bb5bbf05-7a13-5e3a-9d27-540c8c16dcca- task_revision_id
- 1
- config / split
- / test
initial import