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pow:problem4f20 [2020/10/26 23:07] mazur |
pow:problem4f20 [2020/11/04 00:02] (current) mazur |
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+ | <box 80% round orange|Problem 4 (due Monday, October 26)> | ||
+ | Jack and Jill play the following game which results in a 6 digit number: | ||
+ | Jill starts by picking a non-zero digit, the first digit of the number. | ||
+ | Then Jack and Jill alternate picking the next digits, each time they can | ||
+ | choose any digit which has not been used before. Jack wins if the 6 | ||
+ | digit number is a prime, Jill wins otherwise. For example, suppose Jill picks 8, then Jack picks 0, then Jill | ||
+ | picks 9, then Jack picks 4, then Jill picks 6, and finally Jack picks 1. | ||
+ | We get the number 809461, which is a prime number, so Jack wins. | ||
+ | Which player has a strategy to win | ||
+ | regardless of how the other plays? | ||
+ | </box> | ||
+ | |||
+ | Only one solution was received, form Yuqiao Huang. His solution analyses many cases, and some of them are | ||
+ | left for the reader. A shorter solution | ||
+ | is provided in the following link {{:pow:2020fproblem4.pdf|Solution}} |