May 4–May 10, 2010
Problem
In a theater, 50 people watch a very boring play. The play was so
boring that every single person fell asleep once (only once!).
At the end of the play, two actors make the following statements:
Actor 1: During the play, there was at least one moment in which
eight or more people were asleep simultaneously.
Actor 2: In the theater, there is a group of at least 8 people in
which no pair of people slept simultaneously.
Although we can't say which actor is telling the truth, we do know that at least one of them is. Why?
Solution
List of solvers
Lloyd Sakazaki, Dod Moshe, Eric Bensley, Peiyush Jain, Yusuke Tsutsumi, Benny Zhang, Kevin Sonnanburg, Congpa You, Jason Shaw, Tien Nguyen, Mike Goodman, Aakarsh Gottumukkala, Jonathan Cross.
Congpa You wins the prize!