Water Sort Puzzle & Solver
Pour colours until every tube is one shade — and see why one spare tube leaves most deals impossible while two solved every fill tried.
Click a tube to lift its top colour, then click where to pour it. It only goes onto the same colour or into an empty tube, and only as far as there is room.
One spare tube is not “nearly enough” — it is a coin flip, then worse
The obvious guess is that one empty tube gives you room to work and a bigger puzzle just takes more moves. Neither half is true. Searching random fills exhaustively, the share that can be solved at all with a single spare tube falls off a cliff:
| Colours | Solvable with one spare tube | Sample | |
|---|---|---|---|
| 3 | 75.6% | 500 | |
| 4 | 46.2% | 500 | |
| 5 | 28.4% | 500 | |
| 6 | 9.6% | 250 | |
| 7 | 6.4% | 250 |
At four colours it is already a coin flip. By seven, fifteen deals in sixteen are impossible before you touch them — not hard, impossible, with no sequence of pours that finishes. And with no spare tube at all, nothing is solvable, because there is nowhere to pour.
And the second tube fixes it completely
Add one more empty tube and the failures stop. Across 1,560 random fills from 3 to 8 colours, every single one could be solved. Not most — every one, at every size tried.
That is measured rather than proved, so it is worth stating as measured: 1,560 out of 1,560, with no counterexample found. But the gap between one tube and two is not a matter of degree. One tube is a constraint that gets tighter as the puzzle grows; two tubes is enough room that the size stops mattering at all.
Which is why every commercial version of this game hands you exactly two — and why setting the picker above to one produces puzzles that may simply have no answer. The solver will tell you when that happens rather than leaving you to grind at it.
How to use
- Click a tube to lift its top colour, then click where to pour it.
- It only pours onto the same colour or into an empty tube.
- Try one spare tube to see how often a deal is simply impossible.
- Ask for the solution — it finds the shortest one, or says there is none.
Frequently asked questions
How many empty tubes does water sort need?
Two. With one spare tube the share of random deals that can be solved at all falls from about seventy-five per cent at three colours to six per cent at seven. With two, every one of 1,560 random fills from three to eight colours could be solved.
Why do water sort puzzles sometimes have no solution?
Because a random fill is not guaranteed to be solvable, and with only one spare tube most are not. It is not a matter of difficulty — there is genuinely no sequence of pours that finishes. A well-made puzzle is checked before it is handed to you, which is what this page does.
Does a bigger puzzle just take more moves?
Not with one spare tube. The share that can be solved at all collapses as colours are added, so the constraint gets tighter rather than the puzzle getting longer. With two spare tubes the size stops mattering.
What are the rules of water sort?
Each tube holds four units. You may pour the run of colour at the top of one tube onto a tube whose top is the same colour, or into an empty one, and only as much as there is room for. You win when every tube is a single colour or empty.
Can you solve it with no empty tubes at all?
No. With every tube full there is nowhere for a pour to go unless two tubes already happen to match on top, and no random deal in the test could be solved that way. The empty tubes are the whole mechanism.
Is the two-tube result proved?
No, measured — 1,560 fills from three to eight colours, with no counterexample found. It is stated as a measurement rather than a theorem, because that is what it is. The gap between one tube and two is still not a matter of degree.
How does the solver work?
Breadth-first search over tube arrangements, treating two arrangements as the same when the tubes only differ in order. That makes the search finite and returns the shortest solution rather than merely a solution.
Does this send anything anywhere?
No. The puzzles and the solver both run entirely in your browser.
🔒 This tool runs entirely in your browser. Nothing you enter is uploaded, logged, or stored.