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:
  1. Remove one counter from the pile of 6,
    leaving a pile of 1, a pile of 1, and a pile of 5.
  2. Remove one of the piles of 1,
    leaving a pile of 1 and a pile of 6.
  3. 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.
  4. 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.

Links:

Math Games

Mr. P's Puzzles and Games Page