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Omni-MATH / We have an n-gon, and each of its vertices is labeled with a number from the set {1,…,10}. We know that for any pair of distinct numbers from this set there is at least one side of…

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problem

We have an nn-gon, and each of its vertices is labeled with a number from the set {1,…,10}\{1, \ldots, 10\}. We know that for any pair of distinct numbers from this set there is at least one side of the polygon whose endpoints have these two numbers. Find the smallest possible value of nn.
Plain-text mathematical notation (without MathML)
We have an n-gon, and each of its vertices is labeled with a number from the set {1,…,10}. We know that for any pair of distinct numbers from this set there is at least one side of the polygon whose endpoints have these two numbers. Find the smallest possible value of n.
Original LaTeX notation
We have an $n$-gon, and each of its vertices is labeled with a number from the set $\{1, \ldots, 10\}$. We know that for any pair of distinct numbers from this set there is at least one side of the polygon whose endpoints have these two numbers. Find the smallest possible value of $n$.

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Source and history

task_id
a616a3db-ef1b-5fde-93df-5630a9d7b405
task_key
test--a616a3db-ef1b-5fde-93df-5630a9d7b405
task_revision_id
1
config / split
/ test

Official source

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