Question 37
A pond has $2020$ lily pads arranged in a circle. At time zero, two frogs (Anthony and Clare) share the same lily pad. Every minute, Anthony jumps over $99$ lily pads in an anti-clockwise direction, to land on a pad $100$ removed from where the jump started. At the same time, Clare jumps over $100$ lily pads in a clockwise direction, to land on a pad $101$ removed from where the jump started.
What is the first time that Anthony and Clare are again within five lily pads of each other?
What is the first time that Anthony and Clare are again within five lily pads of each other?