This website contains problems from math contests. Problems and corresponding tags were obtained from the Art of Problem Solving website.

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Found problems: 2

1989 ITAMO, 2
Tags: combinatorics , round table
There are $30$ men with their $30$ wives sitting at a round table. Show that there always exist two men who are on the same distance from their wives. (The seats are arranged at vertices of a regular polygon.)

2011 Bosnia And Herzegovina - Regional Olympiad, 2
Tags: round table , combinatorics
At the round table there are $10$ students. Every of the students thinks of a number and says that number to its immediate neighbors (left and right) such that others do not hear him. So every student knows three numbers. After that every student publicly says arithmetic mean of two numbers he found out from his neghbors. If those arithmetic means were $1$, $2$, $3$, $4$, $5$, $6$, $7$, $8$, $9$ and $10$, respectively, which number thought student who told publicly number $6$