How to solve Aquarium puzzles

What is Aquarium?

Aquarium is a grid-based logic puzzle where you fill irregularly shaped regions with water to satisfy row and column clue counts. The twist: water inside each region obeys gravity. It fills from the bottom up and stays level across the full width of the aquarium at any given row. Fill one cell and every cell below it in that same aquarium column fills automatically. Leave one cell empty and everything above it in the same column must also be empty.

The puzzle has no Wikipedia article, no janko.at lexicon entry, and almost no documentation anywhere in English. It exists primarily on puzzle-aquarium.com, which hosts daily puzzles in sizes up to 15×15. The origin is unclear — it appeared in puzzle communities sometime in the 2000s, likely in Eastern European or Japanese contest circles, but there is no confirmed first publication. It is not a Nikoli creation.

The four rules

1. Row and column clues: Each row and column has a number outside the grid. That number is the total count of water-filled cells in that line. If the clue is 0, the entire line is dry. If the clue equals the grid size, every cell in the line is water.
2. Aquarium regions: Thick borders divide the grid into irregular regions. Each region is one aquarium. Cells inside the same aquarium share a water level.
3. Water fills from the bottom: Water is subject to gravity. Within any aquarium, water fills the lowest rows first and rises uniformly. You cannot have a water cell with an air cell below it in the same aquarium column.
4. Binary state: Every cell is either water or air. There are no partial fills, no “maybe” states in the solution. The puzzle has exactly one valid assignment.

How to play

Click or tap a cell to fill it with water (shown in blue). Click again to mark it as air (shown with an X or left empty, depending on your display settings). Click a third time to clear it back to undecided. The clue numbers update as you go, turning green when a line reaches its target count and red when it exceeds the target.

You can also use keyboard controls: arrow keys to navigate, Space to cycle the cell state. The hint button highlights the next cell that can be logically determined, along with a short explanation of the technique used.

Worked example: 6×6 grid

Picture a 6×6 grid divided into five aquariums. The row clues from top to bottom are 2, 4, 3, 6, 5, 4. The column clues from left to right are 3, 5, 2, 4, 6, 4.

Step 1 — Scan for extremes. Row 4 has a clue of 6, which equals the grid width. Every cell in row 4 is water. Column 5 has a clue of 6 — fill it entirely too. That alone resolves 11 cells (row 4 has 6 cells, column 5 has 6 cells, minus the 1 overlap).

Step 2 — Propagate water levels. Every water cell in row 4 means that all cells below it in the same aquarium column must also be water. If an aquarium spans rows 3 through 6 in a particular column, and row 4 is filled, then rows 5 and 6 in that column are also filled. Propagate column 5 similarly.

Step 3 — Check column counts. Column 3 has clue 2. After propagation, count how many cells in column 3 are already water. If two cells are filled, mark every remaining cell in that column as air. Repeat for each column.

Step 4 — Use forced fills. Row 2 needs 4 water cells. After the propagation pass, suppose 2 are filled and exactly 2 undecided cells remain. Both must be water. Fill them and propagate again within their aquariums.

Step 5 — Clean up. By this point most cells are resolved. Check any remaining undecided cells against their row and column clues. Verify the water-level rule holds in each aquarium. Done.

Solving techniques

1. Row/column counting

The simplest technique. If a row or column clue is 0, mark every cell in that line as air. If the clue equals the grid width, fill every cell. These extreme cases show up frequently on easy grids and give you a solid starting position even on harder ones.

2. Water-level propagation

When you fill a cell, gravity takes over. Every cell below it in the same aquarium column must also be water. On a practical level: look at the aquarium as a set of vertical strips. If you fill a cell at row 3, rows 4, 5, 6, etc. in that strip are automatically water. This is the signature mechanic and produces the biggest cascades of new information.

3. Empty-level propagation

The inverse of water-level propagation. If a cell is air, everything above it in the same aquarium column must also be air. Water cannot float. This is less flashy than the downward cascade but equally powerful — marking one cell empty can clear an entire column of an aquarium in one move.

4. Over/under counting

Before committing to a water level in an aquarium, check what it would do to the affected rows and columns. If filling an aquarium to level 4 would push column 2 past its target, that level is too high. If leaving the aquarium empty would make row 5 impossible to reach its target, some water is required. This kind of guess-and-check-without-actually-guessing narrows the options on medium and hard grids.

5. Forced fills

When a row or column needs N more water cells and exactly N undecided cells remain in that line, all of them must be water. Fill them and propagate. This technique triggers constantly in the mid-solve phase and chains well with water-level propagation.

6. Forced empties

When a row or column has already reached its target count, every remaining undecided cell in that line must be air. Mark them empty and propagate upward through their aquariums. Together with forced fills, this pair resolves most medium puzzles without requiring any deeper reasoning.

7. Cross-constraint analysis

The technique that separates hard puzzles from medium ones. A single aquarium spans multiple rows and columns. Setting its water level affects all of them. At higher difficulties, you need to reason about how the water level in one aquarium interacts with the remaining capacity in shared rows and columns, which constrains the possible levels in neighboring aquariums. These chains can run four or five aquariums deep on expert and einstein grids.

Difficulty levels

Aquarium on ThePuzzleLabs comes in five sizes:

• Easy (6×6): 4 to 6 aquariums. Row/column counting and basic propagation solve the whole grid. Good for learning the water-level rule.
• Medium (8×8): 6 to 8 aquariums. Forced fills and forced empties become necessary. Aquariums start sharing more lines.
• Hard (10×10): 8 to 12 aquariums, some irregular. Over/under counting enters the picture. Multiple plausible water levels per aquarium need to be narrowed down.
• Expert (12×12): Up to 16 aquariums across 144 cells. Cross-constraint analysis is the main technique. Chains of reasoning span several aquariums.
• Einstein (15×15): Up to 22 large, irregular aquariums. Deep multi-step deduction with no guessing. The hardest aquarium puzzles published anywhere online.

Aquarium vs similar puzzles

Nonogram is the most obvious comparison. Both give you row and column numbers and ask you to fill cells. The difference: Nonogram clues describe consecutive runs of filled cells, so you track multiple segments per line. Aquarium clues are a single total count. The difficulty in Aquarium comes from the water-level rule within irregularly shaped regions, which Nonogram lacks entirely.

Binairo shares the binary-state model — every cell has exactly two possible values. Both puzzles use row/column constraints to drive deductions. Binairo adds a “no three in a row” rule and a row-uniqueness constraint; Aquarium adds the water-level physics within irregular regions. Different flavors of the same underlying idea.

Thermometers is the closest mechanical relative. Both involve “filling to a level” within constrained regions. Thermometers uses straight or L-shaped tubes; Aquarium uses irregularly shaped regions. Aquarium is more complex because the regions can wrap around corners, creating interactions between rows and columns that straight tubes avoid.

Common mistakes

Forgetting the water-level rule. Water must be level across the full width of an aquarium. If you fill a cell in the middle of an aquarium without checking the cells directly below it in other columns of the same aquarium, you will almost certainly create an invalid state. Always propagate downward when you fill.

Leaving gaps in aquarium columns. Water cannot float above air. If a cell at row 5 is water and a cell at row 3 in the same aquarium column is air, that is impossible — row 4 can't be in a valid state regardless of what you put there. When you empty a cell, propagate upward immediately.

Ignoring 0-clue rows and columns. A clue of 0 means zero water cells in that entire line. This eliminates large chunks of the grid instantly and propagates through aquariums via the empty-level rule. Scan for zeroes first.

Frequently asked questions