# Take a look at my aquarium

This is intended as a gentle introduction to one of my current favourite puzzle types: Aquarium.

The puzzle is played on a rectangular grid divided into regions called "aquariums" (delineated by thick black lines). Your aim is to "fill" each aquarium with water up to a certain level or leave it empty, by shading cells according to the following rules (adapted from puzzle-aquarium.com and Cracking the Cryptic):

1. Within an aquarium, cells that are located in the same row are either all shaded or all unshaded.
2. When a row is shaded in an aquarium, all cells positioned lower than that row in the same aquarium must be shaded as well.
3. The numbers outside the grid indicate how many cells are shaded in the respective row or column. There can be regions without any shaded cell.

Below are two Aquarium puzzles of my own devising. The first can be solved relatively straightforwardly by applying the rules given above; the second is (just a little) more difficult and introduces a couple of additional techniques for solving puzzles of this type.

TASK: Solve both 11x11 Aquarium puzzles below, then combine the two solutions to tell me what are you likely to see when you look into my aquarium?

• Super excited to have a look! Oct 4, 2020 at 23:39

First, some basic deductions:

In any "10" row or column, at least one cell must be filled in any region with 2 or more in that row/column. (For a row, this turns out to mean that all cells in that row are filled; for a column, this means that the bottom one is.)
Similar logic holds for other nearly-full rows/columns, with rooms occupying more of the row or column.

We can then eliminate some cells in very small-numbered rows and columns, especially those that are partially filled.

And repeat:

Fill in more cells that will have to be filled:

And block off more cells that have to be empty:

And repeat again:

Fill in more cells that will have to be filled:

Block off more cells that must be unused:

And now we come to an interesting step:

Consider the 9 on the right puzzle's fifth row. It must skip exactly two cells in its row. Three of its cells force the 2 below it to be completed, so it must use exactly one of those three. This means that all the cells that are not linked in the rows should be filled in the 9, and empty in the 2.
This completes two 10 columns.

Now we can do something else similar, after a bit more work:

The same trick can be repeated with the second and third columns in the right puzzle. The 4 only has one space left, and the 7 must fill at least one cell that extends into the 4. So this lets us fill in the other cells in the 7 column, and finishes off a lot more of the puzzle with help from the sixth row.

The same trick can be repeated on the [4 9] columns in the left puzzle: this completes some rows near the bottom, which helps us finish off the left side...

These steps complete the puzzle with just the usual deductions afterwards. About halfway through, it looks like this:

And the solutions to the puzzles:

Now, overlaying the two puzzles, we see that

we are likely to see GRAVEL in your aquarium!

• All correct :) There are (naturally) a few instances where you could have resolved some points of the logic in earlier steps, but that's just because the nature of this puzzle type means there's often separate simultaneous logic at play, and your focused approach is probably clearer than resolving all at once (e.g. after your first spoiler you could resolve the LH puzzle's bottom right corner knowing that the two together in row 10 must be shaded as one of the two shaded spaces required for the row has been found). The 2-9 step in puzzle 2 was the key one, and you nailed that :) +1
– Stiv
Oct 5, 2020 at 9:48
• @Stiv Yep, that point about the logic is true! I did notice that in a few cases, I saw something that I could've resolved much earlier. Figured this was clear enough, though. Nice puzzles!
– Deusovi
Oct 5, 2020 at 16:40