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: 52

2023 Spain Mathematical Olympiad, 5
Tags: combinatorics , Spain
We have a row of 203 cells. Initially the leftmost cell contains 203 tokens, and the rest are empty. On each move we can do one of the following: 1)Take one token, and move it to an adjacent cell (left or right). 2)Take exactly 20 tokens from the same cell, and move them all to an adjacent cell (all left or all right). After 2023 moves each cell contains one token. Prove that there exists a token that moved left at least nine times.

2019 Spain Mathematical Olympiad, 1
Tags: Spain , Problem Sets , combinatorics
An integer set [i][b]T[/b][/i] is orensan if there exist integers[b] a<b<c[/b], where [b]a [/b]and [b]c[/b] are part of [i][b]T[/b][/i], but [b]b[/b] is not part of [b][i]T[/i][/b]. Count the number of subsets [b][i]T[/i][/b] of {1,2,...,2019} which are orensan.