Why a juice stall?

Colored layers in clear cups look a lot like the drinks counter at a hawker centre, so we built this sorting puzzle as a juice stall. Every flavor has its own color and a fruit icon on each layer, which helps players who find some colors hard to tell apart.

Sorting puzzles usually end with a quiet tick. We wanted a payoff you can see. Fill a cup with one flavor and it gets a straw and a slice of fruit, then slides down to the served counter. Finish the order and the counter is full. Singapore’s hawker culture was added to UNESCO’s list of the Intangible Cultural Heritage of Humanity on December 16, 2020, and a juice stall felt like a friendly corner of it to borrow.

A bit of real sorting puzzle history

Where the liquid sorting puzzle first came from is hard to pin down. Most of what’s online is app store marketing, and we found no reliable source for who made the first one. Its older relative is easy to date. In 1883 the French mathematician Édouard Lucas presented the Tower of Hanoi and credited it to an “N. Claus de Siam”. That name is an anagram of “Lucas d’Amiens”.

It has the same feel as a cup of juice. You move only the top piece, one disk at a time, and never a bigger disk onto a smaller one. With n disks the shortest solution takes 2ⁿ − 1 moves, so 8 disks need 255. The game came with a booklet telling a legend about priests moving 64 golden disks in a temple at Benares.

In 2022, Takehiro Ito and nine co-authors presented a paper on the ball and water versions of these puzzles at a computer science conference called Fun with Algorithms. They proved that a starting position can be sorted with ball moves exactly when it can be sorted with water moves. They also proved that deciding whether a large puzzle can be solved at all is NP-complete. In plain words, nobody knows a quick method that works on every big puzzle. So a computer search checked all 60 of our orders before we shipped them, and that search is how the game knows the fewest pours possible.

The three shifts

• Morning, orders 1 to 20: 3 or 4 flavors and two empty cups.
• Lunch rush, orders 21 to 40: 5 to 7 flavors, cups in two rows.
• Evening, orders 41 to 60: 8 to 10 flavors and up to 12 cups.

How to play

• Tap a cup to lift it, then tap another cup to pour into it.
• Juice pours only onto the same flavor or into an empty cup. Each cup holds 4 layers, and matching layers on top pour together, as many as fit.
• A cup with 4 layers of one flavor gets a straw and goes out to the served counter. Serve every flavor to finish the order.
• Undo as often as you like, or restart the order.
• Once per order you can add an extra empty cup. It costs one star.
• Finish close to the fewest possible pours for three stars. Your stars save on this device.
• On a keyboard, the arrow keys move between cups and Enter or Space lifts and pours.
• 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 counter

Keep a cup empty for as long as you can. It is your most useful tool. Fill it too early and you lose your best move.

Look at the bottoms. A flavor sitting at the bottom of a cup already has a home. Collect it there.

Count before you pour. Three mango layers into a cup with room for two leaves one behind. Sometimes that buries a flavor you need.

Undo is free. Pours you take back don’t count toward your stars. If you get stuck, step back a few pours and try another cup.

Your turn

The morning shift is open at the top of this page, with three flavors and two empty cups. Lift a cup and pour the first order.