Combinatorics · Combinatorial games · Invariants · Parity · Floor function
Andraz and Breda cut two long strips out of a newspaper, of lengths \(a\) and \(b\), to play a game with. A move consists of choosing one of the strips and cutting a piece of length \(d\) off it, so that this strip becomes shorter by \(d\); the piece length \(d\) is fixed and the same for every move. The player who is the first to be unable to cut off a piece of length \(d\) loses. Andraz gallantly lets Breda begin.
Determine how the lengths of the strips decide who wins.
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Slovenian High School Mathematics Competition for Vega Awards (MaSSA), drzavno (national) round 2001, 1. letnik, category A, problem 4. Organized by DMFA Slovenije (Society of Mathematicians, Physicists and Astronomers of Slovenia). Source