January 22–January 28, 2008
Problem
There are 10000 people in a stadium, and a (very large) number is shown to everyone. The first person says the number is divisible by 1; the second says the number is divisible by 2; a third says the number is divisible by 3. This continues until the last person says the number is divisible by 10000. If exactly two consecutive people lied, who were they?
(Just to clarify, there are exactly two liars, and they happen to be consecutive. Everyone else is telling the truth.)
Solution
here.
List of solvers
Ian Zemke, Steve Wilmarth, Kris Reed (Undergraduate), Tristram Bogart, Dustin Moody, Jacob Lewis, Gary Raymond, Robert Bradshaw, Alan Jamison (Graduate), Marina Meila (Faculty), Rich Bauer (Alumni).
The winner this week is Robert Bradshaw!