There's a game in Simon Tatham's puzzle collection where you have to roll a cube around a board to pick up "paint" on each side. That uses noncommutativity, but might not use 3D space as much as you want, https://www.chiark.greenend.org.uk/~sgtatham/puzzles/js/cube.html On Thu, 11 Oct 2018 at 15:56 Mike Stay <metaweta@gmail.com> wrote:
I think such a game would be possible in the style of the various games involving the orientation of rolled pig knuckles relative to each other. The modern version my family has is called "Pass the Pigs" (https://en.wikipedia.org/wiki/Pass_the_Pigs). In that game, there's a score for each configuration, but one of the more common configurations causes you to lose all your accumulated points for that turn, so you're constantly faced with the decision of whether to roll again or to pass the dice to the next player and keep the points you've accumulated so far. On Thu, Oct 11, 2018 at 8:22 AM James Propp <jamespropp@gmail.com> wrote:
Colm Mulcahy's Hamilternion Card Games page
http://www.mathsireland.ie/hamilternion
made me wonder if there are any games that (a) hinge on the fact that 3D rotation is noncommutative and (b) require only ordinary dice.
One idea I like is that we can have one die act on another: if the first die has its m-face facing upward (for m between 1 and 6), we rotate the second die ninety degrees clockwise around the face that shows an m.
Note that the operations of the form "rotate this die ninety degrees clockwise around the face that shows an m" generate a group. It's not the usual way we think about rotation groups, since the specified axes are carried along by the object. A fun way to see that this is still associative is to imagine that the operation is "hold the object still
and
rotate the rest of the universe ninety degrees counterclockwise around the face that shows an m".
To make a game that's fun to play, we'd probably want to incorporate a random element. But hey, we have dice!
To make a game that's fun to play, we'd probably want players to be able to score "points". But hey, we have dice!
Anyone want to suggest a game along these lines that's got elegantly simple rules and is fun to play? Maybe I'll try out a few such games at the upcoming Celebration of Mind.
Jim Propp _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
-- Mike Stay - metaweta@gmail.com http://reperiendi.wordpress.com
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