I would like to submit a "starting point" for the flipping pancakes puzzle.

After looking at the puzzle, I found that I could reliably "fix" the stack every time by using the following method:

Click the largest pancake. This puts it on top. Then click the bottom pancake. This puts the largest pancake on the bottom.

Ignore the bottom (largest) pancake, and repeat this process until the stack is correct.

This allows for 2 flips for each pancake, until the end stage, at which time the final two pancakes can be righted with only one flip, instead of 4 (two each). This gives us a total number of flips of 2n- 3, where n is the number of pancakes.

There may be better methods, but this simple one may serve as a "starting point", since we know any limit must be 2n-3 or less. Any more complex proofs are probably outside of my ability to decipher, much less derive.

Anyone else care to "lower the bar"?

Dave Arnett

Copyright © 1996-2008 Alexander Bogomolny

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