Outcomes of Partizan Euclid
Neil A. McKay, Richard J. Nowakowski · Zenodo (CERN European Organization for Nuclear Research) · 2012
partizan euclid is a game based on the Euclidean Algorithm. The outcome of any position (p, q) is determined by a single path of the game tree; this path has connections to the furthest integer continued fraction of p/q. We convert the question of 'Who wins?' to a word problem, then give a list of reductions that reduces the word/position to one of 9 positions.