January 16, 2018
Problem of the Week
Tuesday, January 16, 2018
Attention! No one has solved the following problem. 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? In order to save the gnomes, equip each of them with the color wheel below. Each gnome should darken the two colors that he or she does not see and connect them by the shortest path along the circumference. What decision making procedure can you give the gnomes that will save them?
