Two runners start on opposite corners of a square field with side 1 km, and run around the edge with integral speeds in the clockwise direction. In terms of these speeds, when will they be the same distance apart as when they started?
(In reply to
solution, I think by Charlie)
Well, that doesn't seem right, Charlie. If one runner runs at 2 km/hour, and one runs at 3km/hr, then after 2 hours they have run 4 and 6 sides respectively, and they are at the same corner. They need to run 4 hours to be at opposite corners, because the difference in the sides they run needs to be a multiple of 4. After 4 hours they have run 8 and 12 sides respectively, and for the first time since they started they are as far apart as they can be.
counterexample
