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Successor Rules for Flipping Pancakes and Burnt Pancakes

The theoretical advanced in pancake flipping, discusses in the August 2020 issue of mini-AIR, were not the end of the story.  Further advances can be found in this study:

Successor Rules for Flipping Pancakes and Burnt Pancakes,” Joe Sawada and A. Williams, Theoretical Computer Science, vol. 609, part 1, 4 January 2016, pp 60-75. The authors, at the University of Guelph and at Bard College at Simon’s Rock, report:

“A stack of n pancakes can be rearranged in all n! ways by a sequence of flips, and a stack of n ‘burnt’ pancakes can be rearranged in all… ways by a sequence of… flips. In both cases, a computer program can efficiently generate suitable solutions. We approach these tasks instead from a human perspective. How can we determine the next flip directly from the current stack? How can we flip the minimum or maximum number of (burnt) pancakes overall? What if we are only allowed to flip the top… (burnt) pancakes?… For the third question, we prove that solutions almost certainly exist for pancakes and burnt pancakes using only these three flips.”

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