Water-sort puzzles: use an empty tube without wasting moves

Define the pouring rule before planning

A sorting strategy is only useful when it matches the rules of the board. In this example each tube holds two units. You can pour onto an empty tube or onto a matching top color. A pour transfers as many consecutive units of the top color as the destination can accept. You cannot pour onto a different color, and the goal requires each color to be gathered in one full tube, leaving the spare tube empty. Partially filled single-color tubes do not count as finished in this model.

We write each tube from bottom to top. [R, B] means red is underneath blue; the accessible color is B. The empty list [] is a completely empty tube. Letter labels matter: the reasoning works without needing to distinguish red from blue visually. These conventions describe our example, not every liquid-sorting game.

A three-pour solution you can check by hand

Start with A = [R, B], B = [B, R], and C = []. There are two red units and two blue units, so the final state can use two full tubes and leave one empty. The first move must use C because the full tubes have no capacity.

Pour A into C. That exposes red in A, creating a destination for the red on B. Pour B into A, completing the red tube. Finally pour C into B to join the blues. The board is solved after three pours: both used tubes are full and monochrome, and C is empty. Check the goal after each move with the explicit win rule; the spare tube must not be filled.

Step   Move     A         B         C
0      start    [R, B]    [B, R]    []
1      A → C    [R]       [B, R]    [B]
2      B → A    [R, R]    [B]       [B]
3      C → B    [R, R]    [B, B]    []

• Read the top entry of the source before each pour.
• Check both matching color and remaining capacity at the destination.
• Stop as soon as the stated goal is satisfied.

Total empty capacity is not the same as a useful empty tube

The example always has two unused units of capacity across the board. After the first pour, that capacity is split between A and C. Yet only A can receive red and only C can receive blue. Counting empty cells alone would miss this restriction.

An empty tube accepts any color under these rules. A partly occupied tube accepts only its top color. Moving a blue unit into an empty tube spends that flexibility, but it can still be an excellent move if it reveals a red unit with an immediate destination. Preserve flexibility for a purpose; do not refuse every move that uses a spare tube.

Recognize a genuinely blocked position

Consider the same two mixed tubes without C. Both are full, so no pour is legal even though each color appears exactly twice. The obstruction is capacity, not a shortage of matching colors. With a third tube available, the same color inventory has a solution.

In a larger puzzle, distinguish no legal moves from legal moves that merely cycle. If you pour a unit into a spare tube and immediately pour it back, the board returns to the same state. Record the arrangement before spending an undo or a hint; a repeated arrangement is evidence that your plan is circling.

Adapt the method when a game changes the rules

Some variants move one unit per tap, allow pouring onto any color, or declare partial monochrome tubes finished. If partial monochrome tubes are accepted, our starting board already meets that different goal after the second pour: A = [R, R], B = [B], C = [B]. Those differences change which moves are legal and when the goal is met. Our three-pour solution applies only to the rule set above.

Before using this method elsewhere, check the transfer size with one reversible move. If an animation moves a whole run, count destination capacity in units rather than in clicks. If there is a timer, determine whether it runs during animations before deciding that faster tapping is useful. A screenshot showing a timer cannot establish how that timer behaves.

Rule clarification and an interactive check

On October 20, 2026, we clarified that the three-pour example requires full single-color tubes. The earlier wording only required single-color contents, which could be satisfied after two pours with blue split between B and C. This is a correction to our model explanation, not a new test of any game.

Try the teaching board above: illegal pours do not consume a move, Undo restores the previous board, and Explain next move computes a shortest continuation under the stated rules. It operates locally in the page, without an account, storage, or a third-party game service.