Flipping pancakes with mathematics

Demonstration of the primary operation. The sp...

Demonstration of the primary operation. The spatula is flipping over the top three pancakes, with the result seen below. In the burnt pancake problem, their top sides would now be burnt instead of their bottom sides. (Photo credit: Wikipedia)

Not so much a full-blown news headline today but it was an article commemorating the 80th birthday of an American professor of mathematics who proposed the “pancake-flipping” problem which still remains unsolved today.  It’s also of interest because Bill Gates wrote a paper on it!  So if you ever have a stack of pancakes for breakfast spare a thought for Jacob Goodman.


Flipping Hell

Order from disorder.
The pancake stack’s in disarray.
How many flips to arrange the stack
back to an ordered way?
Jacob Goodman
(aka Harry Dweighter)
proposed the problem,
(so easy to state),
back in nineteen seventy-five.
But forty years later
it’s still very much alive and kicking,
it hasn’t been solved,
it needs some licking.

Bill Gates resolved to have a go
and showed with absolute certainty
an upper limit of ‘5n plus 5, all over three’.
But the problem persists,
no formula exists,
it resists the best minds in the game.
So if you’re seeking fame,
want to make your name,
make it next year’s resolution,
flipping pancakes ‘til you find a solution.




13th November 2013 – headline from the Guardian

Notes:  “Flipping pancakes with mathematics.”  On the 80th birthday of Jacob E Goodman, a mathematician at the City College of New York, let’s remember him under the pseudonym Harry Dweighter and the unsolved problem he proposed almost forty years ago.  In around 1975, Goodman was at home folding towels for his wife. The final pile was somewhat messy, so he decided to restack the folded towels in order of size, smallest folded towel at the top, biggest at the bottom. The problem was that there was no room for a second pile, so he was forced to flip over the top few towels, reassess the situation, then flip over a few more from the top, and so on.  He recalls how a curious problem crossed his mind: “How many flips would I need in the worst case? I thought it was interesting enough to send to the American Mathematical Monthly, but a more ‘natural’ setting seemed to be pancakes.”  Thus the so-called pancake sorting problem was born. How many flips are required to turn a disordered stack of pancakes into an ordered stack?

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