About Pancake Stack
The pancake puzzle imagines a cook tidying a stack of pancakes, smallest on top, with nothing but a spatula: slide it under any pancake and flip everything above it. It was set as a mathematics problem in 1975, and finding the fewest flips for every stack turned out to be hard; a young Bill Gates wrote a research paper about it in 1979. The burnt version adds a twist, with a burnt side on each pancake that must end up facing down. This page has seven stacks, from four pancakes to eight and two burnt stacks, each solved in advance by a program.
How to play Pancake Stack
- Tap a pancake to slide the spatula under it: it and every pancake above it flip over together, so their order turns upside down.
- Sort the stack with the smallest pancake on top and the biggest at the bottom.
- In the burnt puzzles each pancake is burnt on one side and a flip turns it over: finish with every burnt side facing down.
- The fewest possible flips earn three stars. Your progress is saved on this device only.
Tips & strategy
- The simple method: flip the biggest pancake that is out of place to the top, then flip it down into place. That never takes more than two flips per pancake.
- Look for pancakes already next to their neighbour in size, and keep those pairs together.
- In the burnt puzzles every flip turns a pancake over, so one that is burnt side up needs an odd number of flips and one that is burnt side down an even number.
- In the burnt puzzles the top pancake can be flipped on its own, a quick way to turn it the right way up.
Pancake Stack: questions and answers
How many flips does it take?
Never more than 2n − 3 flips for n pancakes with the simple method, and often fewer. Any stack of six can be sorted in 7 flips, and any stack of eight in 9.
What is the burnt pancake problem?
The same puzzle with a burnt side on each pancake: every flip turns the lifted pancakes over, and the stack is only done when they are sorted with every burnt side down.
Is my progress saved?
Yes, in your browser on this device: the stacks you have sorted, your stars and your best result for each.