Differences

This shows you the differences between two versions of the page.

--- pow:problem4f20 [2020/10/26 23:06]
mazur created
+++ pow:problem4f20 [2020/11/04 00:02] (current)
mazur
@@ Line 1: / Line 1: @@
+<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}}