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Partitionaing a Square

Source: India Postals 2015 Set 3

November 7, 2015
combinatorics

Problem Statement

Suppose a m×mm \times m square can be divided into 77 rectangles such that no two rectangles have a common interior point and the side-lengths of the rectangles form the set {1,2,3,4,5,6,7,8,9,10,11,12,13,14}\{1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14 \}. Find the maximum value of mm.
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