Research on the Tower of Hanoi, a toy for mathematics education. 100 circle will be divided into two parts:

1, the solution of the Tower of Hanoi and the algorithm of the Tower of Hanoi, 100 cycle and 1000 cycle will produce different solutions respectively, and the upper limit can reach 22009 1 cycle.

2. The algorithm of the Tower of Hanoi, whether it is 100 or 1000, works out a series of operations that can complete the movement of the Tower of Hanoi through recursive iteration, so as to reduce the number of times required for the movement as much as possible.