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

Tags were heavily modified to better represent problems.

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Found problems: 2

2005 IMO Shortlist, 6
Tags: graph theory , evan admits orz , combinatorics
In a mathematical competition, in which $6$ problems were posed to the participants, every two of these problems were solved by more than $\frac 25$ of the contestants. Moreover, no contestant solved all the $6$ problems. Show that there are at least $2$ contestants who solved exactly $5$ problems each. [i]Radu Gologan and Dan Schwartz[/i]

2005 IMO, 6
Tags: combinatorics , graph theory , evan admits orz
In a mathematical competition, in which $6$ problems were posed to the participants, every two of these problems were solved by more than $\frac 25$ of the contestants. Moreover, no contestant solved all the $6$ problems. Show that there are at least $2$ contestants who solved exactly $5$ problems each. [i]Radu Gologan and Dan Schwartz[/i]