Puzzle #4: Lewis Carroll’s Pillow Problem
To most, Lewis Carroll is best known as the whimsical author of Alice’s Adventures in Wonderland, but did you know that he was also an avid puzzler and published mathematician? Among his many contributions was a book of mathematical puzzles that he called “Pillow Problems.” They are so named because Carroll devised them in bed to distract himself from anxious thoughts while falling asleep.
The challenge: You have an opaque bag containing one marble that has a 50/50 chance of being black or white, but you don’t know which color it is. You take a white marble from your pocket and add it to the bag. Then you shake up the two marbles in the bag, reach in, and pull a random one out. It happens to be white. What are the chances that the other marble in the bag is also white?
Don’t be deceived by the simple setup. This puzzle is famous for defying people’s intuitions. If you struggle to crack it, think it over while falling asleep tonight. It might at least quell your worries.
Find the solution at the bottom of this page.
