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Board Division

Source: Mexico National Olympiad 2011 Problem 5

June 22, 2014
geometryrectangleinductioncombinatorics proposedcombinatorics

Problem Statement

A (2n−1)×(2n+1)(2^n - 1) \times (2^n +1) board is to be divided into rectangles with sides parallel to the sides of the board and integer side lengths such that the area of each rectangle is a power of 2. Find the minimum number of rectangles that the board may be divided into.
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