Discussion: Though there is not a full and rigorous proof here this student demonstrates a novel way of approaching the problem by recasting it as a game in which there are two players each with a collection of one pound weights that they can put on respective sides of the scale. Player one begins with a weight already on the left side and players can skip turns. Player one has 98 (reflecting that the last box was black and the first weight has already been placed in the scale) and player two has 100. Player two wins if the scale ever balances. What is missing is that even though player one begins ahead, player two has more weights (100 to 99, counting the one initially on the scale) and therefore at some point must draw even before moving ahead. This is best done by using a variant of mathematical induction, the pigeonhole principle - going to the first instance in which player two is a ahead - immediately preceeding this it must have been a tie.

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