Nim - anyone know how to win at this game?

Question

5,4 ,3 match game

Answer 1

Yes i do know how to win this game

Answer 2

The perfect strategy for Nim is to return the board to a state where the count of each bit in the binary representation for each number is even.

3= 2+1

4= 4

5= 4+1

So there's currently 2 4's, 1 2, and 2 1's.  You have an odd number of 2's.  Get rid of one 2, by taking 2 from the 3 pile.  That leaves the opponent at 5,4,1, which is a losing position.

If you want to understand the theory here, read http://en.wikipedia.org/wiki/Sprague%E2%...

Answer 3

Yes, I do.