Puzzle Clouds. How to solve?

Puzzle ‘Clouds’. An example of solving.

Step-by-step analysis of the puzzle https://en.grandgames.net/clouds/id185469

Translation of the post https://en.grandgames.net/post/432380


1. At the beginning we populate with crosses all cells of the column with zero. Also, filled cells cannot exist one by one. So, if a filled cell lies beside an empty column or a border of the field, we need to fill its vertical (horizontal) neighbor. This rule is applicable to the cells 3-5 (3rd row from the top, 5th column from the left) and 8-8.

2. Now the row #3 contains 3 filled cells while 4 cells are required. It is obvious that they form clouds 2-2. So, all cells except for the neighbors of the cell 3-8 are empty. The row #5 must contain two cells. It means that all cells of this row are empty, except for the neighbors of the cell 5-5. Hence, cells 4-1 and 4-2 are empty too, because a valid cloud cannot have one-cell height.

3. Each one from rows #7, #9 and columns #1, #2 must contain 7 filled cells. Empty cells split each of them to the 2-cell and 6-cell groups. It is obvious that there are only two possible variants of the cloud groups: 2-5 and 2-2-3. Hence, each 2-cell group must contain a cloud, and the row #1 is fully defined.

4. Cells 2-6 and 4-6 must be empty, otherwise two different clouds would touch each other. Thus, the row #4 contains two 2-cell clouds. So, cells 4-4 and 4-5 belong to the same cloud, and the cell 4-8 must be filled to guarantee existence of the second cloud.

5. The cell 5-4 must be filled to crеate a rectangular cloud. Hence, the row #5 is fully defined. The cell 6-6 must be empty to avoid touching clouds. The column #6 must contain 3 filled cells. Obviously, these 3 cells must belong to the same cloud, so, the cell 9-6 is filled.

6. The row #9 must contain 2-5 or 2-2-3 clouds. Columns #6 and #7 cannot contain the same cloud, because they must contain 3-cell and 2-cell clouds respectively, so the common cloud cannot be rectangular. Therefore, the row #9 must contain clouds grouped as 2-2-3. Considering that the cell 9-6 is filled, it is possible to place these clouds only as 2-3-2 starting from the left. Cells 7-7, 8-7, 9-7 and 10-7 are empty to avoid touching clouds, cells 6-7 and 11-7 are empty to avoid clouds with one-cell height.

7. The row #8 contains a single empty group where a 3-cell cloud can be placed. The same logic is applicable to the 2-cell cloud from the column #7. We can mark empty cells using the same criteria as at the previous step.

8. Now rows #6, #7, #10 and columns #1, #2 are fully defined. Each of the columns #4 and #5 must contain one more filled cell, the row #2 must contain 2 more filled cells, all other rows and columns are fully defined. Hence, cells 2-4 and 2-5 belong to the cloud. The puzzle is solved!