Suppose that we vary the payoff to the winning player in the game of nim so that

Question:

Suppose that we vary the payoff to the winning player in the game of nim so that the payoff is n dollars when n is the number of legal moves made before a terminal position is reached. Find the payoff to the first player if the initial position consists of
a) Two piles with one and three stones, respectively.
b) Two piles with two and four stones, respectively.
c) Three piles with one, two, and three stones, respectively.