IBM Ponder This #073 · May 2004

This month's puzzle evolved from a suggestion of Michael Brand.
It is a twist on Edouard Lucas' "Towers of Hanoi" puzzle.

To be considered for publication, please supply answers for BOTH parts of the puzzle.

Part 1:
There are three pegs, labelled "A", "B", "C"; and 64 disks of different sizes, numbered from 1 (smallest) to 64 (largest). At no time does a larger disk sit atop a smaller one. We are allowed to move disks, one at a time, from peg to peg, as long as this size rule is obeyed.

When we first see these pegs, "A" has 35 disks, "B" has 18, and "C" has 11. A card next to the pegs indicates that the minimum number of moves required to move all disks to one peg is 3141592653589793238. What disks are on "C", and what disks are on "B"? (The answer is not unique.)

Please submit your answer in a plaintext message (no attachments) in the following format:

C: 2,5,22,23,24,29,30,34,36,40,59
B: 1,3,6,7,8,9,11,14,15,18,19,31,35,43,48,49,51,56

recalling that "1" is the smallest disk.
(The commas may be replaced by spaces.)

Part 2:
A computer program is used to move all 64 disks from peg A to peg B in the fastest route. After several iterations, someone stops the program. The program displays, after every step, the identity of the top disk on each of the three pegs (overwriting the old values as it does so), so, after the program stopped, all you can see is the current state of these. Is this enough information in order for you to determine what the next move should have been? Prove your claim.

As usual, each answer is expected to be your own work.
Computer assistance is allowed, but the answer can be attained by hand.

Solution

Best opened after a real attempt

To be added.