Circle Elimination
People stand in a circle and one leaves at every count. Predict who is left at the end, then watch.
Tap who will be left
How to play
Tap the person you think will be left at the end. Then press "Start": counting begins at person 1, and every time the count is reached, one person leaves. "Remove one" goes a step at a time and "Auto" plays to the end. You can change the number of people and the counting step.
Learn more
This is called the Josephus problem, after a story about the first-century historian Flavius Josephus. When every other person leaves, there is a pattern. Write the number of people in binary and move the leading 1 to the end: that gives the survivor. For 41 people, 101001 becomes 010011, which is person 19. The table below shows the answer for each group size. For steps of 3 or more there is no such simple pattern; a program works the answer out step by step.