1. NIM game is a game with multiple piles of match sticks with the two players taking turns to remove 1 pile or part of 1 pile. The person getting the last stick wins. In the class I had shown how (1, 1) and (2, 2) are losing configurations (i.e. the person facing two piles of 2 and 2 sticks will lose). a) Prove that (3, 4) is a winning configuration. Show how the 1s player can win if she / he plays with a pile of 3 sticks and another pile of 4 sticks. Draw game tree if necessary. Is (1, 2, 3, 4) a winning configuration or losing configuration? This one means 4 piles with 1, 2, 3, and 4 sticks respectively. Explain and show the moves. b)