May 28, 2019
Problem of the Week
Tuesday, May 28, 2019
Arnold and Betty are joined by Carol. The three are wondering if they should form a band called the Three Musketeers. Arnold places six separate pieces of string in his hand and closes his fist, leaving six dangling ends on one side and six dangling ends on the other. The three now take turns tying two loose ends together on one side, then two loose ends together on the other, alternating back and forth until all loose ends are tied (six knots in all). They will form the band if the six strings now form one closed loop. They will start three solo careers if they form 3 closed loops. What is the probability that they form the Three Musketeers? What is the probability that they embark on three solo careers?