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… 3, 4, 5, 6}. (c) Let N = {1, 2, . . . , n} be the set of first n ≥ 2 integers. What is the maximum size of a sum-free subset of N as a function of n? (d) Give an example of a maximum size sum-free subset of N that is also product-free. 1 Problem 2. In each of the following three games, players take turns. That is, player 1 starts, then player 2, then player 1, and so on. For each of the following three games, determine which player has a winning strategy: player 1, player 2, or neither. If there is … shaped mountain with a circular base with radius 20 and length of the sides equal to 60. The plan is to build a track for a sightseeing train around the mountain, which starts at A, at the bottom of the mountain, and ends up at B, which is exactly 10 away from A in the uphill direction. The track goes around the mountain exactly once, and should be covering the shortest possible distance. (a) What is the length of this track? (b) Looking at the picture carefully, you can see that a part of this … apple pies, to share with her visitors Bob and Carol. (a) On Friday evening Bob is there, but Carol is stuck in the traffic. Hav- ing waited for two hours Carol still hasn’t arrived. So Alice and Bob decide they go ahead with the first apple pie anyway. First Alice takes half of the apple pie. Then Bob takes half of the half that remains. Then Alice takes half of what is still left. Then Bob takes half of what is left. And so they continue, on and on, taking turns and always taking half of what …