you the conditions of this task. There are 3 pivots: A, B, C. Initially, n disks of different diameter are placed on the pivot A: the smallest disk is placed on the top and every next one is placed in an increasing order of their diameters. The second and the third pivots are still empty. You have to move all the disks from pivot A to pivot B, using pivot C as an auxiliary. By one step you can take off 1 upper disk and put it either on an empty pivot or on another pivot over a disk with a bigger diameter. Almost all books on programming contain a recursive solution of this task. In the following example you can see the procedure, written in Pascal. Procedure Hanoi (A, B, C: integer; N:integer); Begin If N>0 then Begin Hanoi (A, C, B, N-1); Writeln(‘диск ’, N, ‘ from ‘, A, ‘ to ‘, B); Hanoi (C, B, A, N-1) End End; The number of step Disk From To Combination 0. AAA 1. 1 A B BAA 2. 2 A C BCA 3. 1 B C CCA 4. 3 A B CCB 5. 1 C A ACB 6. 2 C B ABB 7. 1 A B BBB It is well known that the solution given above requires (2n –1) steps. Taking into account the initial disposition we totally have 2n combinations of n disks disposition between three pivots. Thus, some combinations don’t occure during the algorithm execution. For example, the combination «CAB» will not be reached during the game with n = 3 (herein the smallest disk is on pivot C, the medium one is on pivot A, the biggest one is on pivot B). Write a program that establishes if the given combination is occurred during the game.
