Martin Gardner published this puzzle in his “Mathematical Games” column in Scientific American in February 1979. You’re blindfolded and sitting before a lazy susan. On each corner is a glass. Some are right side up and some upside down. On each turn you can inspect any two glasses and, if you choose, reverse the orientation of either or both of them. After each turn the lazy susan will be rotated through a random angle. When all four glasses have the same orientation, a bell will sound. How can you reach this goal in a finite number of turns?

SelectClick for Answer 
This algorithm will do it in five turns:
 Choose a pair of glasses that are diagonally opposite and set both right side up.
 Choose two adjacent glasses. At least one must now be right side up. If the other is upside down, turn it right side up as well. If the bell rings, you’re done; if not, then only one glass is still upside down.
 Choose a diagonally opposite pair. If one is upside down, turn it up and you’re done. If both are right side up, turn one upside down. Now two glasses are upside down, and these two must be adjacent.
 Choose two adjacent glasses and reverse the orientation of both. If the bell doesn’t sound then there are now two glasses upside down, and they’re diagonally opposite one another.
 Choose a diagonally opposite pair and reverse both. The bell will sound.
