January 9, 2018

A dragon has imprisoned six gnomes in his cave and said, "I have seven caps, colored with each color of the rainbow. Tomorrow morning I will blindfold you and put a cap on each of you, and hide the last cap. Then I will take the blindfolds off, and you'll be able to see what color everyone else is wearing but you cannot talk to one another. Then without letting the others hear, tell me the color of the hidden cap. If at least 3 of you guess correctly, I'll free you all. If not, I'll eat you for lunch." How can the gnomes come up with a strategy that saves them?