This is an ancient puzzle. There is a stack of 64 discs (ranging from the smallest to the largest from top to bottom), all through one pole; while the other two poles remain empty. The object is to rebuild the pile of discs from the original pole to another pole by following these two simple rules:

- You can only move ONE DISC at a time.
- You can NEVER place a larger disc on top of a smaller disc.

Folklore:

It has been said that if anyone can ever complete all the necessary moves (by hand) to solve this puzzle, the world will come to an end.

Myth:

The story would be TRUE, if someone could live the 600 billion years it would take to do 18-billion billion moves it requires to solve this puzzle (assuming one second per move, and that this person never ever goes to sleep).

Reality:

If such a person existed, the world would be gone long before he could ever even finished the puzzle. The Earth is 5 billion years old, and only has another 5 billion left, since our Sun will burn out by that time. As a matter of fact, our entire UNIVERSE is only 15 billion years old, and is expected to collapse in another 15 billion years. Do the math.

Why so many moves? As it turns out, there are:

(2^64)-1 moves

...in the original TOWERS OF HANOI. But what if we reduce the number of discs? Then the number of moves would reduce down to:

(2^n)-1 moves.

You guessed it. The smaller 'n' is, the lesser the moves, and it goes down dramatically. If there were only 8 discs, then there are only:

(2^8) - 1 = 255

...moves, which would only take about 4 minutes to solve (at one move per second).

Solving the Towers:

You can solve the Towers of Hanoi by becoming the HUMAN ALGORITHM. First of all, imagine that the entire tower of discs alternate in color (black, white, black, white...). Now, along with the 2 original rules, all you have to do is obey a few more restrictions:

- You must always move SMALLEST DISC first, and on EVERY OTHER MOVE
afterwards. Otherwise (
*in-between every other move*), move the next-to-the-smallest AVAILABLE disc. - You can only place a BLACK disc directly on top of a WHITE disc. If you cannot, then place it on an empty base.
- You can only place a WHITE disc directly on top of a BLACK disc. If you cannot, then place it on an empty base.

See you in 600 billion years!

Out-of-the-box Solution (for an 8-disc set):

1C, 2B, 1B, 3C, 1A, 2C, 1C, 4B

1B, 2A, 1A, 3B, 1C, 2B, 1B, 5C

1A, 2C, 1C, 3A, 1B, 2A, 1A, 4C

1C, 2B, 1B, 3C, 1A, 2C, 1C, 6B

1B, 2A, 1A, 3B, 1C, 2B, 1B, 4A

1A, 2C, 1C, 3A, 1B, 2A, 1A, 5B

1C, 2B, 1B, 3C, 1A, 2C, 1C, 4B

1B, 2A, 1A, 3B, 1C, 2B, 1B, 7C

1A, 2C, 1C, 3A, 1B, 2A, 1A, 4C

1C, 2B, 1B, 3C, 1A, 2C, 1C, 5A

1B, 2A, 1A, 3B, 1C, 2B, 1B, 4A

1A, 2C, 1C, 3A, 1B, 2A, 1A, 6C

1C, 2B, 1B, 3C, 1A, 2C, 1C, 4B

1B ,2A, 1A, 3B, 1C, 2B, 1B, 5C

1A ,2C, 1C, 3A, 1B, 2A, 1A, 4C

1C, 2B, 1B, 3C, 1A, 2C, 1C, 8B

1B, 2A, 1A, 3B, 1C, 2B, 1B, 4A

1A, 2C, 1C, 3A, 1B, 2A, 1A, 5B

1C, 2B, 1B, 3C, 1A, 2C, 1C, 4B

1B, 2A, 1A, 3B, 1C, 2B, 1B, 6A

1A, 2C, 1C, 3A, 1B, 2A, 1A, 4C

1C, 2B, 1B, 3C, 1A, 2C, 1C, 5A

1B, 2A, 1A, 3B, 1C, 2B, 1B, 4A

1A, 2C, 1C, 3A, 1B, 2A, 1A, 7B

1C, 2B, 1B, 3C, 1A, 2C, 1C, 4B

1B, 2A, 1A, 3B, 1C, 2B, 1B, 5C

1A, 2C, 1C, 3A, 1B, 2A, 1A, 4C

1C, 2B, 1B, 3C, 1A, 2C, 1C, 6B

1B, 2A, 1A, 3B, 1C, 2B, 1B, 4A

1A, 2C, 1C, 3A, 1B, 2A, 1A, 5B

1C, 2B, 1B, 3C, 1A, 2C, 1C

Notation:

1 = smallest disc

8 = largest disc

A = move disc to left column

B = move disc to middle column

C = move disc to right column

...assuming that the initial column of discs is on the left.