To solve Aquarium, count each row and column, and remember that water runs down. A line numbered 0 is all dry; a line with just enough room is all water. Every time water goes in, it spreads across its tank and fills the rows below; every time a square is marked dry, everything above it in the tank is dry too. When the easy counts run out, ask what water (or dryness) in a square would force, and whether the numbers still fit. Six techniques cover every puzzle in the game.
New to Aquarium? Read the Aquarium rules first. This page assumes you know the two rules: each row and column holds its number of water squares, and water lies flat in every tank.
1. Water lies flat
Water in a square fills its tank across that row and on every row below. A dry square makes its tank dry across that row and on every row above. Do this every time you mark a square.
2. Finished lines
A row or column that already has all its water is dry everywhere else. One with just enough open squares left is water everywhere else. Numbered 0 and full-length lines are the extreme cases.
3. Too much water
Water can’t go in just one square: it brings its whole tank row with it, and everything below. If that would put more water in some row or column than its number allows, the square is dry. Watch for tall tanks in columns with small numbers.
4. No room
The same idea the other way round. A dry square dries its whole tank row and everything above. If that would leave some row or column without enough open squares for its number, the square holds water.
5. Every arrangement
When a line is crossed by just a few tanks, list the ways their runs can add up to its number, keeping water flat. Any run that’s water in every way holds water; any run that’s dry in every way is dry.
6. What if
When nothing else works, pick a tank row and suppose it holds water (or stays dry). Follow what that forces with the techniques above. If some row or column can no longer meet its number, the supposition was wrong, and it goes the other way. The what-if page follows one through a real puzzle.
How often each technique is needed
We solved every one of the game’s 150 levels by following the hints, which always use the simplest technique that works. This is how many times each technique was used, on average, per level:
| Technique | Easy 6×6 | Medium 8×8 | Hard 10×10 |
|---|---|---|---|
| Water lies flat | 5.0 | 8.6 | 11.2 |
| Finished lines | 8.9 | 12.9 | 16.7 |
| Too much water | 0.9 | 4.9 | 11.3 |
| No room | 0.1 | 1.0 | 7.0 |
| Every arrangement | 0 | 0.1 | 1.4 |
| What if | 0 | 0 | 2.4 |
Finished lines and flat water do most of the work at every size. Too much water appears on 17 Easy levels, 41 Medium and every Hard one. Every arrangement is almost only for Hard (42 levels), and what-if is never needed on Easy or Medium, and on 39 of the 50 Hard levels.
An 8×8, solved in three stages
This is Medium level 50 from the game, the hardest Medium level.
Stage 1: a tall tank, and the rows it unlocks
There’s no row or column numbered 0 or 8 here, so start with a tall tank. Column 4 is numbered 3, and the tank that starts in row 3 runs down through rows 4, 5 and 6 of that column. Water in its row 3 would put four water squares in column 4. So row 3 of that tank is dry.
Row 3 is numbered 7, so with one dry square it’s water everywhere else. The water spreads down its tanks, and more checks for too much water settle rows 4 and 5.
Stage 2: every arrangement of row 1
Row 1 is numbered 3 and crosses three tanks, with runs of 2, 3 and 3 squares. The only ways to make 3 are one of the runs of three. The run of two can never be part of it, so it’s dry.
Stage 3: the rest
From there it’s mostly counting: 9 finished lines, 3 rounds of flat water, 2 for too much water, 2 for no room and 2 more arrangements finish the grid.
When you get stuck
- Spread every mark. Water fills across and down its tank; dry spreads across and up.
- Count every line again, columns as well as rows. A line that’s just changed may be finished or have just enough room.
- Look for tall tanks. In a column with a small number, water high in a tall tank is usually too much.
- List the ways for a line crossed by few tanks. Two or three runs rarely make a number more than one or two ways.
- Don’t guess. Every puzzle here can be finished by logic.