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Paraguayan National Olympiad 2007, Level 3, Problem 2

Source:

September 1, 2014
geometry

Problem Statement

Let ABCDABCD be a square, such that the length of its sides are integers. This square is divided in 8989 smaller squares, 8888 squares that have sides with length 11, and 11 square that has sides with length nn, where nn is an integer larger than 11. Find all possible lengths for the sides of ABCDABCD.
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