Matches Piles Puzzle

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1 Response

  1. Gagan says:

    if the number of matches in all boxes is same , like (2,2,2) or (3,3,3) , then the first person to pick will definitely lose.
    otherwise , he can always win.

    proof is simple by induction. we can see that (0,1,1) (1,1,1) , (0,1,2) (1,1,2) (1,2,2) are all winning positions for the first player.
    so if the first player is on (2,2,2) – he can only go to one of these in 1 step and then its the second players turn who will def. win
    similarly if (a,b,c) a>=b >=c is the starting position with a>c , the the first player can simply pick (a-c) matches from the first pile and (b-c) matches from the second pile to go to (c,c,c). now its 2nd persons turn who def. looses.