These are examples of She-Loves-Me-She-Loves-Me-Not. If you can get access to Een Pak Met Een Korte Broek, Papers presented to H.W.Lenstra, you'll find one with subtitle Relatives of two game of Lenstra, which lists Sympler, Fitted Carpets, The octal games .3 (take a bean from a heap), .5 (take a bean if it's isolated or one from a larger heap which must be left as two non-empty heaps), .7 (take a bean for a heap, possibly splitting the remainder into 2 heaps) (or 3 heaps, 4 heaps, ...), 4.0 (split a heap into 2 non-empty heaps), 4.2 (split a heap into 2 non-empty heaps, or take a bean fro a larger heap), 3030303... (take any odd number of beans), 4.01, 4.04, 4.05, 4.21, 4.24, 4.25, .30X, .50X, .70X, where 0<X<8, Brussels Sprouts, Jocasta, Impartial Childish Hackenbush, ... (most of these are in Winning Ways). R. From: math-fun [math-fun-bounces@mailman.xmission.com] on behalf of James Propp [jamespropp@gmail.com] Sent: Thursday, November 13, 2014 9:00 AM To: math-fun Subject: [math-fun] Games of no strategy What are fun examples of combinatorial games that (like Conway and Paterson's game of Brussels Sprouts) appear to be games of strategy but whose outcome doesn't depend on what either player does? One of my favorites is Impartial Cutcake, aka the Candy Bar Game. The initial state is a chocolate rectangle, scored into unit squares. On any given turn, a player may take any rectangular piece bigger than a 1-by-1 square and divide it along a horizontal or vertical scoring-line into two smaller rectangular pieces. The two players alternate. When no further divisions are possible, the game ends, and the player who made the last move wins (and, if you like, gets to eat all the pieces). Jim Propp _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun