Problem 4. [15 points) Nika and Yida share an office. In their office, there are two cookie jars that each start with n

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Problem 4 15 Points Nika And Yida Share An Office In Their Office There Are Two Cookie Jars That Each Start With N 1 (83.76 KiB) Viewed 32 times

Problem 4. [15 points) Nika and Yida share an office. In their office, there are two cookie jars that each start with n e z+ cookies. They make a friendly game by the following rules: 1. They take turns and eat cookies from the jars. 2. In one turn, one can only open one of the two jars, but they can take any number of cookies ke Z where 1 <k<n from that jar. 3. One wins the game if he/she takes the final cookie on his/her turn. Nika realizes that she has found a strategy such that Yida is always going to be the one loses the game. With n cookies in each jar, Nika lets Yida take the first turn. First, find Nika's strategy. Then, prove that it works for any number of cookies n by strong induction.