Why water sort puzzles are so satisfying
A water sort puzzle gives you a row of bottles, each holding a stack of coloured layers, and asks you to pour them between bottles until every bottle holds a single colour. It sounds like a task rather than a puzzle. It turns out to be a proper one, because the one rule about pouring limits you far more than it first seems to.
The satisfying part and the hard part come from the same place. Every pour is visible and every sorted bottle stays sorted, so you can see yourself making progress. But every pour also changes which moves are available next, and a careless one can leave you with no move at all.
The rules most versions share
The details vary between games, but most follow the same pattern. Each bottle holds a fixed number of layers. You can only pour the top colour of a bottle, and you can only pour it into a bottle that is empty or whose top colour matches. When you pour, as much of that top colour moves as will fit. The puzzle is solved when each colour has been gathered into a bottle of its own.
Two consequences follow from this. The first is that you can never reach a colour buried under another one until everything on top of it has gone somewhere. The second is that an empty bottle is the only place that accepts any colour, which makes empty space the most valuable thing on the board.
Why it is harder than it looks
Each bottle behaves like a stack: the last layer in is the first one out. Sorting with stacks is a well-studied problem in computer science, and the reason is that stacks are awkward. To free a colour at the bottom you have to put the layers above it somewhere, and those layers then block whatever they land on.
That is why the obvious move is often wrong. Pouring a colour onto its match feels like progress, but if it fills your last empty bottle, or covers a colour you needed next, you may have closed off the only route to the finish. A position can look nearly solved and still be stuck, with every top colour different and no empty bottle to break the deadlock.
The difficulty also grows fast. Adding one more colour means more layers to bury each other and more ways to fill the spare room, so a puzzle with a few more colours than another can be far harder rather than a little harder.
How to get better at it
Look before you pour. Before the first move, check which colours sit at the bottom of each bottle, because those are the ones that will need the most clearing. A bottle whose bottom layer is already the colour you want is a good place to build.
Treat an empty bottle as something you spend, not something you fill. Pour into it only when you know what the pour frees up, and try to get it back soon after. Consolidating two small runs of the same colour into one is usually a good move, because it frees a layer of space somewhere else.
Work towards one finished bottle at a time. A completed bottle is out of the way for good, and it stops that colour from blocking anything again. It is often worth a few moves that look like no progress to get there.
When you are stuck, go back rather than forward. The move that caused the trouble is usually a few steps earlier than the one that revealed it, and it is nearly always the pour that used up your last empty space.
Why it feels good
The appeal is not hard to name. The goal is clear from the first glance, the board shows exactly how far you have got, and the end state is tidy in a way few other puzzles are. There is no hidden information and no luck, so when a puzzle comes out it is because you found the order of pours that works.
