# Tagged Questions

Questions involving the pigeonhole principle, which states that if $n$ items are placed in $m$ containers and $n>m$, then one at least one container has more than one item.

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### Show that there are always two teams who played exactly the same number of games.

So i was given this question. There are 11 teams in a league. Each team can play against the other team only once. Show that there are always two teams who played exactly the same number of games. My ...
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### 7 points on a closed disk, one must be the center

I am trying a pigeonhole strategy for proving this assertion of a MO test: "Given 7 points on a closed disk of radius 1 such that the distance between any two of this points is at least one, then one ...
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### Choosing $7$ numbers from $[1,2,…,11]$ will give us $2$ that have sum $12$.

Choosing $7$ numbers from $[1,2,...,11]$ will give us $2$ that have sum $12$. I tried: There are only $5$ pairings possible: $(7,5),(8,4),(9,3),(10,2),(11,1)$ Suppose I pick $6$, and then not to be ...
### How can we prove that every sequence of $30$ elements from a set of three repeats a subsequence of length 3?
How can we prove that for every series over $30$ elements(included $30$), there must be a "sub" three element series then will repeat itself? (Series's numbers are only $\{1,2,3\}$) Example for a "...