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Aquarium: No Room

A dry square isn’t dry on its own either. It dries its tank’s whole row, and every row of the tank above. If that would leave some row or column without enough open squares for its number, the square holds water.

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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

  1. Pick an open square, and see what keeping it dry would mean: the rest of its tank on that row, and every row of the tank above.
  2. For each row and column that touches, count the water and the squares still open.
  3. If any of them couldn’t reach its number any more, the square holds water (and so does everything below it in the tank).

In a real puzzle

On the 10×10, it’s first needed at step 17. Row 2 is numbered 8. It holds 3 water squares and has 7 open. The tank across columns 8 to 10 has three squares in the row: keeping them dry would leave only 7 squares that could hold water, one short. So those three hold water.

Step 17: no room in row 2 Row 2 is numbered 8. It holds 3 water squares and has 7 open. Keeping the tank across columns 8 to 10 dry would leave only 7 squares that could hold water. So those three hold water. 0 8 4 8 7 8 10 7 3 5 5 7 9 7 6 4 6 7 4 5
Step 17: keeping the right-hand tank dry would leave row 2 one short. It holds water.

How often you’ll need it

On 4 of the 50 Easy levels, 21 Medium and every Hard one: 0.1 times per Easy level on average, 1.0 on Medium and 7.0 on Hard. It’s 4 of the 43 moves on the 10×10 here.

Next steps

Questions

Is this just too much water the other way round?

Yes. Too much water asks what water in a square would force; no room asks what keeping it dry would force. One finds dry squares, the other water.