MathDB
Game: Combining rectangles to make bigger rectangles

Source: XVIII Olimpíada Matemática Rioplatense (2009)

July 23, 2011
geometryrectanglecombinatorics unsolvedcombinatorics

Problem Statement

Alice and Bob play the following game. It begins with a set of 10001000 1×21\times 2 rectangles. A move consists of choosing two rectangles (a rectangle may consist of one or several 1×21\times 2 rectangles combined together) that share a common side length and combining those two rectangles into one rectangle along those sides sharing that common length. The first player who cannot make a move loses. Alice moves first. Describe a winning strategy for Bob.