Problem 1 (The Three-Cap Problem)

One cold winter morning in Maine a mother insists that her three daughters, Ann, Betty, and Cindy wear caps to school and so she randomly picks 3 caps from a pile of 5 caps, three of which are white and two are red. The girls stand in line, one behind the other, waiting for the mother to put on their caps. Cindy stands in the back and can see both of the other girls; Betty stands in the middle and can see Ann who stands in the front; but Ann standing in the front cannot see either of the other girls. The mother then puts a cap on each of the girl's heads. For fun, the mother asks the girls if they can guess the color of their own caps. (The girls know their mother picked the caps from the 5 caps, three white and two red.) Cindy, who is in the back, says she has no idea the color of her own cap. Betty, hearing what Cindy says, also says she has now idea the color of her cap. But Ann, hearing what Cindi and Betty say, says she does knows the color of her cap. How is Ann able to determine the color of her cap ? What is the color of Ann's cap ?

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Last modified on Tuesday, January 12, 1999