Rules for the Towers of Hanoi problem:

• Move the disks from pole 1 (left) to pole 3 (right).
• Only one disk can be moved at a time.
• A larger disk cannot be placed on a smaller disk.
• All disks except the one being moved must be on a peg.

How do we solve this puzzle? (to see how computer scientists think)

• Divide and conquer, recursively.
• Reduce problem size by half at each step: fast solution.
• Reduce problem size by 1 at each step: slow solution.
• Top-down backward-chaining way to think about the problem.
• Bottom-up forward-chaining does not work well (may need extra work, may not reach goal)

The Towers of Hanoi problem shows how a small program can be used to solve a seemingly complicated problem. The key is to divide the problem into smaller parts, solve each turn, and combine the solutions to solve the overall problem.