@Nitish,
I think it fails for this condition

4 heaps with 1,2,1,2

Player 1 starts first with picking 1 coin from heap 1
Player 2 picks 2 coins from heap 2
Player 1 picks 1 coin from heap 3
Player 2 picks 2 coins from heap 4.

Player 2 wins but XOR of the number of coins in each heap is 0(if that is
what you meant).

Thanks,
Immanuel

On Wed, Jun 15, 2011 at 6:40 PM, Nitish Garg <nitishgarg1...@gmail.com>wrote:

> I think that when the XOR of all the coins is zero Player 1 can always win.
>
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