Why pancakes?

The Tower of Hanoi is a pile of disks in different sizes. A stack of pancakes is the pile most people already know, so we moved the puzzle into a café. The stack starts on a hot griddle, and each level is an order: carry every pancake to the customer’s plate, one at a time, and never put a bigger one on a smaller one.

Food has been part of this puzzle for over a hundred years. When Henry Dudeney wrote a version with four pegs, he used cheeses on stools. Our later orders add his fourth spot, plus two café rules of our own: syrup pancakes that can’t go back on the griddle, and customers who change seats partway through.

A bit of real Tower of Hanoi history

The French mathematician Édouard Lucas brought out the Tower of Hanoi in 1883. He put a made-up name on it: “N. Claus de Siam” of the college of “Li-Sou-Stian”. Both are anagrams, of “Lucas d’Amiens” and of Saint-Louis, the school where he taught.

The puzzle came with a legend. In a temple at Benares, priests move a tower of 64 golden disks by the same rules, and when they finish, the world ends. The fewest moves for n disks is 2ⁿ − 1. For 64 disks that is 18,446,744,073,709,551,615 moves. At one move a second, that takes about 585 billion years.

In 1907 Dudeney published The Canterbury Puzzles. Its first puzzle, the Reve’s Puzzle, has eight cheeses of different sizes on four stools. The fourth spot makes the job much shorter, but the best method is hard to see. In 1941 J. S. Frame and B. M. Stewart published a method for any number of pegs. Whether it was the best possible for four pegs stayed unproven until 2014, when Thierry Bousch, a mathematician at Université Paris-Sud, published a proof. For eight pieces on four spots the answer is 33 moves, and our own computer search agrees. For five or more pegs, the method is still only believed to be the best.

The three shifts

• Breakfast, orders 1 to 10: 3 to 5 pancakes, the griddle and two plates. Syrup and seat changes first show up here.
• Brunch, orders 11 to 20: a third plate arrives, with 5 to 7 pancakes.
• Lunch rush, orders 21 to 30: mostly 8 pancakes, with more syrup and more seat changes.

How to play

• Tap the griddle or a plate to lift its top pancake, then tap where it should go. You can also drag it.
• One pancake at a time. A bigger pancake can never sit on a smaller one.
• Serve the order by moving the whole stack to the customer’s plate, marked with 🙂.
• Syrup pancakes, with dark syrup on top, can’t go back on the griddle.
• In seat-change orders the customer moves to the 🪑 plate once the biggest pancake reaches them.
• Undo is free. Each order has 3 hints, and each one shows the best next move.
• Finish close to the fewest possible moves for three stars. The targets show under the score, and your stars save on this device.
• Sound is on to start. Tap 🔊 to mute, or 🎵 for music.
• Earn 3 stickers in this game for your QuickBOP sticker book.

Tips from the griddle

Watch the smallest pancake. On plain orders with two plates, the best solution moves it every other move, always around the same way.

Odd or even picks the first move. With two plates and an odd number of pancakes, the first one goes straight to the customer. With an even number, it goes to the spare plate.

Park a few on the extra plate. With three plates, set some small pancakes aside on one spare, move the rest the two-plate way, then bring the small ones back on top. That is the Frame and Stewart idea.

Plan the seat change. Before the biggest pancake lands, think about where the rest of the stack should be waiting.

Your turn

The griddle is hot and order 1 has three pancakes. Lift the top one and start serving.