Ken's POTW


Nim
In the game of Nim (as I know it) two players each take turns taking any number of sticks from any one of three piles. The winner is the player who takes the last stick.
  1. If the three piles hold 3, 5, and 7 sticks, and it's your turn to play, what is your best move?
  2. If, instead, there are four piles holding 3, 5, 7, and 9 sticks, and it's your turn to play, what is your best move?
  3. Is there a strategy that can be followed to win the game? (Briefly show how it works in the above examples.)
Extra:

Source: Previous puzzle experience. Some parts used as Ken's Puzzle of the Day 2/10/94.


Solution
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