Sort all balls so each tube contains only one type!
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How a puzzle about moving colored balls between tubes descends from a 19th-century toy, a 1970s card game and the logistics of shipping container yards β and why mathematicians only caught up with it in 2022.
The rules fit in a sentence. You have a row of tubes holding colored balls stacked on top of one another. You may lift the topmost ball from any tube and drop it onto an empty tube, or onto a ball of the same color. Sort every color into its own tube and you win.
That is the whole game, and it is almost certainly the most-installed puzzle mechanic of the 2020s. It is also much older than the app that made it famous.
The French mathematician Γdouard Lucas sold the Tower of Hanoi as a toy in 1883, under the pseudonym "N. Claus de Siam" β an anagram of "Lucas d'Amiens". Discs of decreasing size sit on one of three pegs; move them all to another peg, one at a time, never placing a larger disc on a smaller one.
The family resemblance is obvious: a small number of stacks, a legality rule about what may sit on what, and a goal state that requires temporarily making things worse. The difference is what makes ball sort interesting. Hanoi's constraint is a strict ordering β every disc is unique and there is exactly one legal arrangement. Ball sort has interchangeable pieces: four balls of the same color are identical, so the puzzle has an enormous number of equally valid solutions and no obvious recursive structure to exploit. Hanoi has a clean formula for the minimum number of moves. Ball sort, as we will see, has nothing of the kind.
The other half of the lineage runs through patience games. Paul Alfille wrote FreeCell in 1978 for the PLATO educational computer system at the University of Illinois, adapting an older game called Baker's Game. Its innovation was the four "free cells": open slots that hold one card each, used purely as temporary parking while you rearrange the columns.
Anyone who has played ball sort will recognise that immediately. The empty tube is a free cell. The core tension in both games is identical β you have a small, precious amount of scratch space, and the skill lies in planning a sequence of moves that unwinds a tangle without running out of it. Spider Solitaire contributes the other half: building descending runs of matching suit, where placing a card onto a compatible card is the legal move, much as a ball may only land on its own color.
FreeCell reached a mass audience when Microsoft bundled it with Win32s in 1992 and then with Windows 95, where it became the game that taught a generation the pleasure of a puzzle with no hidden information and no clock.
While the mechanic was drifting toward toys, operations researchers were studying it in deadly earnest. In a shipping container terminal, containers are stacked in towers. When a truck arrives for a container buried three deep, the ones above it must be moved somewhere β onto other stacks, because there is nowhere else. Choosing where to put them, so as to minimise the total number of wasteful relocations, is known as the container relocation problem or blocks relocation problem.
It is the same puzzle. Stacks with limited height, a last-in-first-out constraint, a shortage of free space, and a cost paid for every move you make only to undo a previous one. The literature is substantial and still active, with recent work throwing reinforcement learning and branch-and-bound at instances that remain computationally nasty. A crane operator in Rotterdam and a commuter tapping at a phone are, formally, doing the same work.
The version most people have played arrived in 2020, when the Australian studio IEC Global Pty Ltd published both Ball Sort Puzzle and Water Sort Puzzle. The two are nearly the same game with different skins β balls stack discretely; water pours, merges and flows in quantities β and both spread with remarkable speed through the first year of the pandemic.
The mechanic suited the moment and the business model almost perfectly:
What followed was one of the most conspicuous cloning waves the app stores have seen. Search either store today and you will find hundreds of near-identical titles, many sharing template code and differing only in name and icon. The genre's pre-2020 web and Flash history is genuinely murky for this reason β the mechanic is simple enough that it was probably independently reinvented many times before anyone thought to build a business on it.
By the industry's own accounting, the early sort-puzzle category was a modest affair β bare template UI, under about $2M a year, almost entirely ad-funded. The mechanic was enormously popular and barely monetised.
Two years after the boom, a group of Japanese algorithms researchers β Takehiro Ito, Jun Kawahara, Shin-ichi Minato, Yota Otachi, Toshiki Saitoh, Akira Suzuki, Ryuhei Uehara, Takeaki Uno, Katsuhisa Yamanaka and Ryo Yoshinaka β presented Sorting Balls and Water: Equivalence and Computational Complexity at the 11th International Conference on Fun with Algorithms.
They proved three things worth knowing if you are building one of these games:
That first result has a practical edge. Any developer who has tried to compute the true minimum number of moves for a hard level and watched a breadth-first search grind through hundreds of thousands of states has met NP-completeness in person. The honest engineering answer is to stop looking for the optimum and use a fast heuristic estimate instead.
A year later Suthee Ruangwises added a pleasing curiosity: a physical zero-knowledge proof for the ball sort puzzle, presented at Computability in Europe 2023. Using only a deck of cards, you can convince someone that you know a solution to a given level without revealing a single move of it β reportedly the first such protocol for an interactive puzzle involving moving objects.
Having been left as a cheap ad-funded curiosity for years, sort puzzles were rebuilt into a serious commercial category by a series of games that kept the sorting fantasy and threw out the vertical tube.
Block Jam 3D launched in spring 2022 and scaled through 2023, replacing the one-dimensional stack with a 2D board and a limited dock, so that the scratch-space tension moved from "which tube" to "which slot". Hexa Sort, released in 2023, dominated 2024 with hexagonal geometry β more neighbours per tile, so more interconnection β plus automatic sorting and spawning pieces that made a previously static puzzle feel alive. Then in 2025 Grand Games' Magic Sort demonstrated that a polished water-sort game could earn on in-app purchases alone, reportedly taking more than $40M in its first year and calling the whole ad-driven model into question.
The through-line is that every successful variant loosened one constraint of the original β the dimensionality, the tidiness of the board, the staticness of the pieces β while keeping the moment that makes the genre work.
Strip away the business history and a ball sort puzzle is an unusually pure piece of game design.
It has perfect information: nothing is hidden, so every loss is your own fault and every win is earned. It has no time pressure, which makes it legible to players who bounce off anything demanding reflexes. Its state is completely visible at a glance β you can read the entire board in a second, which is why it survives being played in thirty-second bursts. And it has a genuine decision with teeth: the last empty tube is a resource you can spend exactly once before the position closes up on you.
Then there is the completion. A tube filling to a single solid color is a small, unambiguous, physically satisfying event, and a good implementation leans on it hard. That feeling is the entire reason the genre outlived its clones β and it is a straight inheritance from the moment, forty-odd years earlier, when a column of cards in FreeCell finally came clean.