describe the straggy and formula for the puzzzle tower of hanoi
From the moves necessary to transfer one, two, and three disks, we can find a recursive pattern - a pattern that uses information from one step to find the next step - for moving n disks from post A to post C:
First, transfer n-1 disks from post A to post B. The number of moves will be the same as those needed to transfer n-1 disks from post A to post C. Call this number M moves. [As you can see above, with three disks it takes 3 moves to transfer two disks (n-1) from post A to post C.]
Next, transfer disk 1 to post C [1 move].
Finally, transfer the remaining n-1 disks from post B to post C. [Again, the number of moves will be the same as those needed to transfer n-1 disks from post A to post C, or M moves.]
First, transfer n-1 disks from post A to post B. The number of moves will be the same as those needed to transfer n-1 disks from post A to post C. Call this number M moves. [As you can see above, with three disks it takes 3 moves to transfer two disks (n-1) from post A to post C.]
Next, transfer disk 1 to post C [1 move].
Finally, transfer the remaining n-1 disks from post B to post C. [Again, the number of moves will be the same as those needed to transfer n-1 disks from post A to post C, or M moves.]
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