A Mathematician's 3-Step Method for Solving Any Water Sort Puzzle
Why Most Players Get Stuck (And Why They Don't Have To)
Most players approach a water sort puzzle the same way: scan the tubes, find a move that looks legal, make it, and repeat until they either finish or hit a dead end. That is a valid strategy for easy levels. It fails comprehensively on harder ones, and the failure mode is always the same — a board where every tube is a mixed-color tangle with no obvious path forward. At that point, the typical response is to hit undo repeatedly and hope for a better outcome, or to reset the level entirely.
There is a better approach. It comes from computational puzzle theory, specifically from the family of constraint-satisfaction algorithms that computer scientists use to solve problems like Sudoku, map coloring, and — yes — water sort. The three techniques at the core of those algorithms are constraint propagation (eliminate impossible states first), look-ahead (evaluate consequences before committing), and backtracking (when you hit a dead end, reverse to the last decision point and try a different branch). Applied to human puzzle-solving, these translate into three concrete steps that work on any level, from the introductory boards in our water sort library to the hardest configurations in games like Bubble Sorting Deluxe or Ball Sort Puzzle.
This guide walks through all three steps, then applies them to three specific levels from SortFun's catalog. If you want a broader set of tactics that apply across multiple puzzle types, our 10 universal sorting tips cover the full spectrum. But for water sort specifically, the three-step method is the most systematic framework available to a human player.
Step 1 — Constraint Propagation: Clear Single-Color Completions First
Constraint propagation means: before you make any exploratory move, identify and execute every move that is forced. In water sort, a forced move is one where a tube contains a single solid color and there is another tube holding the same color with space to receive it. Completing that transfer does not require any trade-off analysis. It is always correct to do it, and doing it first simplifies everything that comes after.
Here is the key insight: every move you make that is provably correct shrinks the problem space. After you complete all forced moves, the board you are looking at is the real puzzle — the version where every remaining move carries some trade-off. You have eliminated noise. Now you can think clearly.
In practice, scan the board this way before touching anything: look for any tube where all segments are the same color. If that tube is full, it is already complete — ignore it. If it is not full, find every other tube containing that color and count the total segments. If those segments fit into the incomplete tube, you have a forced completion sequence. Execute it.
On Bubble Sort, which uses floating bubble mechanics rather than stacked liquid, the same logic applies: bubbles of matching colors that can be merged without splitting a color group represent forced moves. Clear them before attempting any exploratory moves. The game's early levels are almost entirely solvable by constraint propagation alone — the tricky levels are the ones where no forced moves exist at the start, and you must move to Step 2.
A note on empty tubes: do not use them in Step 1 unless you have to. Empty tubes are your most flexible resource, and spending one in a forced move is sometimes necessary, but spending one on an exploratory move you have not thought through is how boards collapse. Treat empty tubes as precious until Step 3, when you may need them deliberately as staging areas.
Step 2 — Look-Ahead: Count Colors to Find Chokepoints
Once you have cleared all forced moves, you need to identify the chokepoints — the colors or tubes that constrain your remaining options most severely. Look-ahead means evaluating consequences two to three moves deep before committing, rather than acting on whatever looks locally appealing.
The technique is: count how many segments of each color remain on the board, and count the total capacity available to receive each color. A color with ten segments and only one receiving tube is a chokepoint. Any move that blocks that receiving tube — even temporarily — risks deadlock. Identify these colors first, because they must drive your sequencing.
Concretely, do this scan after Step 1: for each color still on the board, count its total remaining segments. Divide by four (the standard tube capacity in most water sort games). That gives you the number of complete tubes that color needs. Now count how many tubes currently have any of that color in the top position (which means they can receive more). If the number of tubes that can receive the color is only barely enough to accommodate all remaining segments, that color is a chokepoint. Prioritize clearing space for it before making moves that serve other colors.
In Bubble Sorting Deluxe, the mid-game levels regularly present boards where two or three colors share only a few viable receiving tubes. The look-ahead step is what separates players who finish those levels cleanly from players who burn through their undo budget. If you are using undo more than twice per level on average, you are skipping Step 2.
The look-ahead technique also applies to ball sort variants. In Balls Sorting Deluxe, which uses a column-based container model rather than tubes, the same chokepoint analysis holds: identify which color has the fewest viable landing columns and plan around it. Our broader guide to ball sort vs. water sort strategy covers how the look-ahead step differs slightly between the two formats.
Step 3 — Backtracking: Working Backwards from a Target State
Step 3 is the one most players never formally apply, even though they do a crude version of it when they spam the undo button. Backtracking, done correctly, is different from random undo usage. It is deliberate: you define a target board state that would unlock progress, then work backwards to identify the sequence of moves that could reach it.
Here is how to apply it in practice. When you are stuck — no forced moves exist, and every exploratory move you can see leads to a worse board — stop. Instead of looking at where you are, ask: "What board state would let me make progress?" Usually the answer is specific: "If tube 3 were empty, I could transfer the red segments from tube 7 into it and unlock tube 5." Name the target state. Now ask: "What sequence of moves gets tube 3 empty?" Work backwards from that goal. You may find that clearing tube 3 requires first moving its current contents — which requires first making space in another tube — which requires a three-move setup sequence you would never have found by scanning forward.
This is exactly how computer backtracking algorithms work. They do not search forward from the current state; they identify a desirable future state and compute the shortest path to it, then verify that the path is legal. The human version is less exhaustive but conceptually identical.
Applied to Sort Them Bubbles, which tends to generate boards with multiple interlocked color clusters in its higher levels, the backtracking step is often the only way through. Identify the color that most needs to consolidate, find the tube state that would allow that consolidation, and work backwards to create it. The path may be four or five moves long, and none of those moves will look like progress when you make them — but they create the conditions for the breakthrough move that follows.
For color sort variants that use horizontal or grid-based layouts rather than vertical tubes, the backtracking target-state question shifts slightly: instead of "what tube state do I need," you ask "what cell or slot configuration do I need." The logical structure is the same.
Worked Example 1: Applying All Three Steps to Bubble Sorting Deluxe
Let's walk through how the three steps apply to a mid-difficulty level in Bubble Sorting Deluxe. Assume the board has eight tubes, six active colors, and two empty tubes at the start. Standard configuration for levels in the 30-60 range.
Step 1: scan for forced completions. Suppose two tubes each hold a single solid color. Execute those transfers first. Now you have six tubes with mixed colors, two empty tubes, and two complete tubes (which you ignore). The board is simpler.
Step 2: look-ahead on remaining colors. Suppose one color — call it orange — has six remaining segments spread across three tubes, and only two tubes have orange in the top position to receive more. Orange is a chokepoint: you need to consolidate it into one or two complete tubes, and you only have two viable receivers. Do not block either of those receivers with a different color. Plan your next three to five moves so that both orange-receiving tubes remain accessible.
Step 3: backtracking. Suppose the orange consolidation is blocked because tube 4 has a purple segment on top of an orange segment. You need to move that purple segment to make orange accessible. Where can purple go? Suppose purple has no other tube with purple on top, but there is one empty tube. You can stage the purple segment in the empty tube temporarily. That burns one of your two empty tubes — which means your subsequent moves must free up a tube before you need a staging area again. Work backwards to verify this chain is feasible before committing. If it is, execute it.
This three-step cycle — force, analyze, backtrack — repeats until the board clears. On a well-designed level, it will clear cleanly. On a level with what puzzle designers call "forced bad-state branching" (a situation where every legal move produces a worse board), the method will at minimum identify the least bad path forward. We examine forced bad-state scenarios in detail in our post on the 7 hardest screw sort levels, which presents similar analytical challenges.
Worked Example 2: Ball Sort Puzzle and the Chokepoint Color
In Ball Sort Puzzle, which uses colored balls stacked in vertical tubes rather than liquid, the three-step method applies with one modification: because balls are discrete objects rather than continuous fluid, the visual separation between colors is clearer, which makes Step 1 faster. Forced completions are easier to spot. The challenge moves entirely into Step 2.
On the harder levels of Ball Sort Puzzle (typically the 70-plus range), the boards are designed so that at least two colors share a single viable tube as their only consolidation point. This is the designer's version of a chokepoint: two colors competing for one resource. Look-ahead reveals this immediately. Once you see it, your job is to sequence the two consolidations so that the shared tube is used once for each color in the correct order — which usually means completing the color with fewer remaining segments first, freeing the shared tube for the more complex consolidation.
Players who skip Step 2 on these levels will almost always make the consolidation in the wrong order, blocking themselves with two or three moves left to go. The undo cost of that mistake is typically four to six moves — which, on a game with limited undo availability, can be decisive.
Worked Example 3: Marbles Sorting and When to Burn an Empty Tube
In Marbles Sorting, the puzzle design tends to generate boards where the correct move often looks wrong because it temporarily makes the board appear more disordered. This is the classic "it gets worse before it gets better" pattern that drives players to undo moves that were actually correct.
The three-step method handles this by making Step 3 explicit. When a move creates apparent disorder — splitting a color group, using an empty tube, creating a tube with two different colors where there was previously one — check whether it was motivated by the backtracking analysis. If you did it because you identified a target state and this was the first move in the path toward it, trust the analysis and continue. If you did it reactively, without a target state in mind, undo it and go back to Step 2.
The willingness to burn an empty tube — using it as a staging area for a piece that needs to temporarily move out of the way — is the key skill in Marbles Sorting's harder levels. The empty tube is not sacred; it is a tool. But spending it correctly means you have already done the backtracking analysis and know that you will free up a tube within the next two moves. Spending it without that analysis is the main cause of dead ends.
If you want to explore more systematic strategies, our complete water sort strategy guide covers additional techniques including how to handle levels with three or more empty tubes (which changes the calculus significantly). For players drawn to the ball-and-tube variant, our ball sort vs. water sort breakdown examines how the strategy differs between the two formats. And if you want to test the method immediately, the water sort section on SortFun has dozens of levels across the difficulty range where these steps apply cleanly.
