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Gluing a 100*100 chessboard - who wins?

Source: All-Russian Olympiad 2006 finals, problem 9.7

May 7, 2006
combinatorics proposedcombinatorics

Problem Statement

A 100×100100\times 100 chessboard is cut into dominoes (1×21\times 2 rectangles). Two persons play the following game: At each turn, a player glues together two adjacent cells (which were formerly separated by a cut-edge). A player loses if, after his turn, the 100×100100\times 100 chessboard becomes connected, i. e. between any two cells there exists a way which doesn't intersect any cut-edge. Which player has a winning strategy - the starting player or his opponent?