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: 1

2022 Vietnam TST, 6
Tags: combinatorics , set theory , important numbers , coloring
Given a set $A=\{1;2;...;4044\}$. They color $2022$ numbers of them by white and the rest of them by black. With each $i\in A$, called the [b][i]important number[/i][/b] of $i$ be the number of all white numbers smaller than $i$ and black numbers larger than $i$. With every natural number $m$, find all positive integers $k$ that exist a way to color the numbers that can get $k$ important numbers equal to $m$.