Each tank crosses a row as a run of squares that are all water or all dry. List the ways the open runs can add up to what the line still needs, keeping water flat. A run that’s water in every way holds water; one that’s dry in every way is dry.
This is one of the Aquarium techniques. Each page shows its technique on the same 10×10 from the game, Hard level 16.
The rule
- Pick a line, and work out how many more water squares it needs.
- List its open runs, each a tank’s squares in the line. In a column, a tank’s lower squares fill before its higher ones.
- Find every way to make the number from those runs.
- Mark any run that’s the same in every way.
In a real puzzle
On the 10×10, it’s first needed at step 24. Row 10 is numbered 5 and already holds 3 water squares, so it needs 2 more. Its open squares fall in runs of 1, 2, 2 and 2. Two can only come from one of the runs of two; the single square never fits. So it’s dry.
How often you’ll need it
Never on Easy, on 1 of the 50 Medium levels, and on 42 Hard ones, 1.4 times per Hard level on average. It’s 1 of the 43 moves on the 10×10 here.