Puzzle #19: Mental Illusions
1. 100 ants fall onto a meter stick at the same time at random locations. Each ant begins walking toward the left or the right end of the stick at random, at a speed of one meter per minute. Ants continue on their chosen course, but any time two ants collide, they both immediately reverse directions and continue walking the opposite way at the same speed. What is the longest amount of time it could take before all of the ants have walked off the end of the stick?
2. A rectangle is inscribed inside a quarter of a circle that is centered at O. Find the length of the rectangle’s diagonal AC.
Find the solution at the bottom of this page.
