Los Angeles Math Circle

1/15 -- Junior Circle: The Hanoi Tower and some things we need to know to play around (Dr. Oleg Gleizer)

Hidden in the jungle near Hanoi, the capital city of Vietnam, there exists a Buddhist monastery where monks keep constantly moving golden disks from one diamond rod to another. There are 64 disks, all of different sizes, and three rods. Only one disk can be moved at a time and no larger disk can be placed on the top of a smaller one. Originally, all the disks were on one rod, say, the left one. At the end, they all must be moved to the right rod. When all the disks are moved, the world will come to an end. (No worries here, it will take the monks a few hundred billion years to complete the task.) In this session, we shall first play with the puzzle and try to figure out the fastest way to solve it. Next, we shall study some auxiliary material needed to better understand the puzzle. This includes place-value numeral systems, like the decimal system we use for counting, the binary system that formed the bedrock of Egyptian multiplication we have learned in the Fall quarter, and pizza slicing as a way to think about fractions.