Mainly to Neil, My email system has been changed, so apologies for any inadequacies. Can do as you wish with the paper. The only nim-sequence that arises is 010101010101010101010.... R. ________________________________________ From: math-fun [math-fun-bounces@mailman.xmission.com] on behalf of Neil Sloane [njasloane@gmail.com] Sent: Thursday, November 13, 2014 12:52 PM To: math-fun Subject: Re: [math-fun] Games of no strategy Since the paper Richard mentions contains A006016, and Een Pak Met Een Korte Broek is very rare, and privately printed, I think we would be justified in adding a scanned copy of his paper as an attachment to A006016. That would be OK with you, Richard, I assume, since you've generally given the OEIS permission to do this sort of thing? Richard, what about other sequences that arise from the paper? The octal games you mention, for instance - can you tell me the A-numbers, or the first few terms, of any of them? (I have a copy of the book, since Andrew Odlyzko and I wrote something in it) Best regards Neil Neil J. A. Sloane, President, OEIS Foundation. 11 South Adelaide Avenue, Highland Park, NJ 08904, USA. Also Visiting Scientist, Math. Dept., Rutgers University, Piscataway, NJ. Phone: 732 828 6098; home page: http://NeilSloane.com Email: njasloane@gmail.com On Thu, Nov 13, 2014 at 11:50 AM, Richard Guy <rkg@ucalgary.ca> wrote:
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).
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