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Cousin of Nim

In this game, two players take turns to take buttons from two different piles,
the winner being the
person to take the last button (similar to the game of Nim, in an earlier
POTW.) On each turn a player must claim either
(a) any number from one pile, or
(b) an equal number from both.
If a game had 4 buttons in one pile and 8 in the other, and it were your
turn to claim, how should you play to be absolutely sure of winning?
What configurations, with 10 or less buttons in each pile, could be
classified as winning configurations, where you could be absolutely
sure of winning?

Source: *Puzzlegrams*, Pentagram Design Limited, 1989, #90.
Used as Ken's POTD 9/9/94.

Solution

Mail to Ken