Homework1Solution.pdf - Stat 155 Fall 2019 Homework 1 Solution Problem 1 1 Analyze the subtraction game with subtraction set{2 4 7 That is for each

Homework1Solution.pdf - Stat 155 Fall 2019 Homework 1...

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Stat 155 Fall 2019 Homework 1: Solution Problem 11. Analyze the subtraction game with subtraction set{2, 4, 7}. That is, for each position ofnchips,n= 0,1,2, . . ., classify the position as aP-position or anN-position. Problem 2: KP 1.1Consider a game of Nim with four piles, of sizes 9, 10, 11, 12.(a) Is this position a win for the next player or the previous player (assuming optimal play)? Describethe winning first move.(b) Consider the same initial position, but suppose that each player is allowed to remove at most 9chips in a single move (other rules of Nim remain in force). Is this anN- orP-position? Solution

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