Aquarium Rules: How to Play, Strategies and Variations

What is Aquarium?

Aquarium is a grid-shading logic puzzle. The grid is split by thick walls into irregular regions called tanks (or aquariums). Your job is to decide which cells are filled with water. Numbers outside the grid tell you how many water cells each row and each column must contain.

The twist is gravity. Water inside a tank always settles at the bottom and lies perfectly flat, so a tank can be empty, full, or filled to some level in between, but never half full on one side and dry on the other. If one cell of a tank is wet, every cell of that tank in the same row is wet, and so is everything in that tank below it.

That single physical idea turns a plain counting puzzle into something with real character. Like a Nonogram, you shade cells to match numbers on the edges, but instead of runs of blocks you are reasoning about water levels, which link cells that can be far apart in the grid.

A short history

Aquarium is a younger puzzle than the Japanese classics such as Sudoku and Light Up. Its exact origin is not well documented, and unlike many grid puzzles it is not usually credited to a single magazine or designer.

It spread mainly through puzzle apps, websites and competition-style puzzle collections, where it found a following among solvers who enjoy number-on-the-edge puzzles but want something with a different flavor. The "water settles at the bottom" rule is so intuitive that newcomers usually understand it at a glance, which has helped it travel.

Today Aquarium sits comfortably alongside other shading puzzles such as Nurikabe and Nonograms. Grids range from gentle 6×6 introductions to large competition grids where the logic chains run across a dozen tanks.

The core rules

A standard Aquarium has four rules. The first two describe the grid, the last two describe how water behaves.

1. 1Shade water cellsEach cell is either water or empty (air). The solution is the set of water cells.
2. 2Match the edge numbersThe number beside each row says how many water cells that row contains. The number above each column does the same for that column.
3. 3Water lies level in a tankInside a tank, water forms one flat surface. If any cell of a tank is wet in a given row, every cell of that same tank in that row is wet too.
4. 4Water settles at the bottomThere are no air pockets under water. If a cell is wet, every cell of the same tank in the rows below it is also wet. A tank may also be completely empty or completely full.

Put the last two rules together and each tank has only a handful of possible states: one per row it spans, plus empty. A tank covering three rows can be empty, filled one row deep, two rows deep or full, and nothing else. Thinking in terms of these levels rather than individual cells is the heart of solving.

A solved example

Here is a 6×6 Aquarium with nine tanks. The numbers on the left count water cells in each row, the numbers on top count them in each column. It has exactly one solution. Try it before looking at the answer on the right.

Start with row 2, which needs five of its six cells. The long tank across its right-hand side supplies four of them, and the other two cells belong to different tanks, so without that long tank the row could reach two at most. The long tank must therefore be filled at least to row 2. Next look at column 6, which needs just one water cell: the long tank already provides it in row 2. So the small tank in the top right corner stays dry, and so does the tall tank on the right, because any water in it would reach the bottom of column 6. With those tanks settled, column 4 needs five water cells, so only one of its cells can stay dry, and the remaining rows fall into place one tank level at a time.

How to play: a step-by-step method

This routine works on any Aquarium and is enough to finish most small grids.

1. List each tank's possible levels. Note which rows each tank spans. Its only options are empty, full, or filled to the top of one of those rows. Small tanks often have just two or three options.
2. Look for the extreme clues. A row or column clue of 0 empties every cell in that line, which also empties every tank cell above them. A clue equal to the line length fills every cell, which fills every tank cell below them.
3. Mark cells as water or air. Shade water and put a small dot in cells you know are dry. A dot is just as useful as a shaded cell, because it rules out every level that would wet it.
4. Push consequences up and down. A wet cell means everything below it in that tank is wet. A dry cell means everything above it in that tank is dry. Apply these after every new mark.
5. Count what each line still needs. Compare each clue with the water already placed and the cells still undecided. When the remaining need equals the remaining space, fill them all. When it is zero, dot them all.
6. Check the whole tank, not just the cell. Filling one cell in a row fills its whole tank row. Before shading, make sure that row of the tank fits every column clue it touches.

Strategies experienced solvers use

Once the basic method is second nature, these ideas will speed you up and get you through harder grids.

Most Aquarium deductions come down to these two moves: counting blocks against clues, and passing information up and down inside a tank. The more fluently you see each tank as a stack of levels, the faster the grid empties. To keep practicing, you can solve Aquarium online at LogicPuzzles.io, which has a new daily puzzle plus unlimited 6×6, 8×8 and 10×10 tank grids.

Popular variations

Standard Aquarium is the version you will meet most often, but a few twists turn up in collections and contests.

• Missing clues. Some row or column numbers are left out. Those lines can hold any amount of water, so you lean harder on the remaining clues and on the tank logic.
• Rectangular grids. The grid does not have to be square. Wide or tall layouts change which clues are easy, since long rows with large clues often fill several tanks at once.
• Large grids. Grids of 10×10 and above with many small tanks, where long chains of block counting replace the quick wins of small puzzles.
• Few, large tanks. Some setters use a handful of big, winding tanks. There are fewer pieces to track, but each level choice affects many rows and columns at once.

Common mistakes

The most common mistake is shading a single cell instead of a whole tank row. It is tempting to drop water into one square to satisfy a clue, but if that cell's tank stretches across the row, the whole stretch fills with it, and the neighboring columns change too.

Second, beginners often leave air under water. If a tank has water at a certain height, every cell of that tank below it must be wet, even if it sits several rows lower and around a corner of the tank's outline.

Third, watch out for tanks with gaps in a row. A tank shaped like a U can have two separate cells in the same row. Water still lies level across the whole tank, so both sides fill together even though they are not side by side.

Finally, solvers sometimes forget the empty option. A tank is allowed to stay completely dry, and in many puzzles several tanks do. Do not assume every tank must hold at least some water.

How Aquarium compares to other puzzles

Aquarium is closest in feel to Nonograms: both give you counts on the edges and ask you to shade cells. The difference is that a Nonogram cares about runs of shaded cells in a line, while Aquarium cares about whole tanks, so the constraints link cells across rows instead of along them.

It also pairs well with Star Battle, another region-based puzzle where row and column counts meet irregular shapes. If you enjoy the counting in Aquarium, Star Battle is a natural next step, and if you like the physical intuition, Light Up offers a similarly visual rule about how light travels across a grid.

Frequently asked questions