With n discs, in other words that there is no quicker way? The solution Can you express m n in terms of m n-1? Can you show that m n is in fact the minimum number of moves needed to solve the puzzle Write m n for the number of moves you need to solve the puzzle with n discs according to this recipe. Your proof now gives you a recipe for solving the puzzle for any number of discs. Now assume that you can move a tower of n-1 discs: does this help you to move a tower of n discs? If yes, then why does this prove that the puzzle can be solved for any number of discs? (A proof that uses this way of thinking is an example of the principle of We've already seen that the puzzle can be solved for n equal to 2 and 3. Hint: Suppose that you have n discs in total. But can you show that it is possible to move a tower consisting of any number of A little thought will show you that moving a tower of three discs is possible also. If you've only got two discs in total, then the puzzle is easy: move the top disc from peg 1 to peg 2, then move the bottom disc from peg 1 to peg 3, and finally move the smaller disc on peg 2 onto the larger disc on peg 3 - done.
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