Hello everyone! Here is our first Math Club Competition question. We will let you know where to submit your solutions to. Please submit by October 14th Our math club currently has N student members. From time to time, students like to tell each other secrets, including their own but also those that were previously told by someone else. To avoid the awkward situation that a student wants to share a secret that the other student already knows, the math club decides to assign each student with a unique membership number from 1 to N and announces the following rule: a student with membership number A is permitted to share a secret with student member B if and only if A(B-1) is a multiple of N. Prove that if all members follow this rule, then no student will be told a secret that he or she already knows. This problem can also be formulated and solved on a graph: let G be a directed graph with vertices 1 through N such that there is an edge going from vertex A to B if and only if A and B are distinct and A(B-1) is a multiple of N. Prove that this graph does not contain a directed cycle. Ready go!
Posted on: Tue, 01 Oct 2013 17:58:57 +0000
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