Some children have made up a simple version of the game “Duck, Duck, Goose”. In this game a group of people stands in a circle, and the person who is “it” taps the first person on the shoulder and says “duck”. The next person is tapped and called “duck” The next person is tapped and called “goose”, and the process is repeated. Every person who is called “goose” must sit down when they are tapped.
If there are a million people in a circle, and they are labeled sequentially from 1 to 1,000,000, and the tapper starts at person 1 going around and around until only one person is left standing, then what is that last person’s number?
E5. Duck, Duck, Goose
This problem was sent to me (as is) by Walter Carter of Seattle.