#### Numbers and Algebra

##### Tower of Hanoi

Legend has it that the world will end when the puzzle is complete. Well, the original puzzle consisted of 64 disks, and the monks in the legendary civilization only moved one disk per day. With this in mind, according to the legend, when will the world end? Solve the puzzle, determine the rule for the Geometric recursion relationship, and calculate the number of days required to complete the 64-disk problem.