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Source: Moldova Junior TST 2008 Day 1 Problem 4

April 11, 2008
combinatorics proposedcombinatorics

Problem Statement

The square table 10×10 10\times 10 is divided in squares 1×1 1\times1. In each square 1×1 1\times1 is written one of the numers {1,2,3,...,9,10} \{1,2,3,...,9,10\}. Numbers from any two adjacent or diagonally adjacent squares are reciprocal prime. Prove, that there exists a number, which is written in this table at least 17 times.
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