Dividing Piles
You begin this game with any number of piles of any number of objects.
On his turn, a player may either (1) divide a pile into 2 piles or
(2) remove one counter from a pile.
Play continues until one player takes the last counter and is the winner.
Strategy:
Move to a postion with an even number of 1 piles and an even number of even piles.
You may leave your opponent with any number of odd piles.
Example:
If there are three piles: a pile of 1, a pile of 1, and a pile of 6,
then a player could do any of the following moves:
- Remove one counter from the pile of 6,
leaving a pile of 1,
a pile of 1, and a pile of 5.
- Remove one of the piles of 1,
leaving a pile of 1 and a pile of 6.
- Split the pile of 6 into 2 piles,
leaving a pile of 1, a pile of 1, a pile of 3,
and a pile of 3.
- Split the pile of 6 into 2 piles,
leaving a pile of 1, a pile of 1, a pile of 4,
and a pile of 2.