The Game of Nim is a famous studied 2 player strategy game. http://en.wikipedia.org/wiki/Nim
There are 3 heaps, and you are given the number of pebbles in each heap. Player 1 and 2 take turns removing pebbles from each heap. Game ends when a player cannot remove any pebbles from any heap, and the last player able to do so is the winner.
Given the number of pebbles in each heap, determine if player-1 will win assuming that both player play their optimal strategy, ie their best possible moves.
For the test case [7 7 7] all of [1 7] [2 7] [3 7] should be valid responses, right? Also you don't have any test cases where the game is not winnable.