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Estonian Math Competitions 2005/2006

Source: Juniors Problem 4

July 30, 2008
combinatorics unsolvedcombinatorics

Problem Statement

A 9×9 9 \times 9 square is divided into unit squares. Is it possible to fill each unit square with a number 1,2,...,9 1, 2,..., 9 in such a way that, whenever one places the tile so that it fully covers nine unit squares, the tile will cover nine different numbers?
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