Three cups problem

The three cups problem is a mathematical puzzle. Starting with three cups place one upside down and two right side up. The objective is to eventually turn all cups right side up in six moves. You must turn exactly two cups over each turn.

Solution

The puzzle is impossible. An even number of cups are facing up and you are allowed to turn two over at a time. Since an even plus an even is an even, not an odd, no number of even flips will ever get all the three cups face up. You need an odd number of cups facing up, so the problem is impossible. The possible version of this puzzle is to start with two cups facing down and one cup facing upward. This is possible. Turn up an even number (two) of cups, and all the cups are facing up; an odd plus an even is an odd (1+2 = 3).

See also

• Parity
• List of impossible puzzles

jagdesh in house, like mouse

External links

• Three Cups Animation
• Three Cups Problem
• Three Cups Problem Student's Handout Along With Explanation