# Snowcaps - A grid deduction puzzle

This winter-themed puzzle is basically an upside-down Aquarium, the idea being that instead of fish tanks being filled with water, the areas are mountains being covered with snow. The goal is to shade "snow" cells in each area according to the following rules:

• On a mountain, cells that are located in the same row are either all shaded or all unshaded.
• When a row is shaded on a mountain, all cells positioned higher than that row on the same mountain must be shaded as well.
• 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.

To get into the spirit of the puzzle, you may wish to use white for shaded cells, and brown for unshaded. This one's not too hard; I hope you enjoy!

TEXT VERSION

   4 2 2 2   9   6 4 5 7
═ ═ ═ ═ ═ ═ ═ ═ ═ ═ ═ ═
║ | | | ║ | | | | ║ | | ║
═ - - ═ - - ═ ═ ═ - - -
║ ║ | ║ | | ║ | ║ | | | ║
- ═ ═ - ═ ═ - - ═ - ═ ═
║ | ║ | ║ | | | | ║ ║ | ║
- - ═ ═ - - - - - ═ - -
║ | | ║ | | | | | | ║ | ║
- - - - - ═ - - - ═ - -
║ | | ║ | ║ ║ | | ║ | | ║
- - ═ - ═ - ═ ═ ═ - - -
5 ║ | ║ ║ ║ | | ║ ║ | | | ║
═ ═ - ═ - - ═ - - ═ - -
║ ║ | | | | ║ | ║ ║ ║ | ║
- - - - - ═ - - ═ - ═ ═
5 ║ ║ | | | ║ | | ║ | | | ║
- ═ - - - ═ - ═ - - ═ -
║ | ║ | | ║ ║ ║ | | ║ ║ ║
- - ═ - ═ - ═ - - - - -
3 ║ | | ║ ║ | | ║ | | ║ ║ ║
- - - ═ - - - ═ - ═ - ═
║ | | | ║ | | | ║ ║ | | ║
- - - - - - - - ═ - - -
4 ║ | | | ║ | | | ║ | | | ║
═ ═ ═ ═ ═ ═ ═ ═ ═ ═ ═ ═


## The final picturesque landscape:

(For all images, open link/click for a larger version)

### 1. Starting small:

To start, a snow cell can be placed in the 9 column as there must be at least one snow cell on that mountain. Next, focus on the clues for the rows. The 3 cannot be made up by the 4 or the 1s, so must be a 3 and this 'greys out' a lot of mountains bottom right. The second 5, must also be a 4 and a 1, so some of the middle mountain can be greyed out.

### 2. Big next step:

As there is now a grey in the 9 column, there must be another snow cell in the bottom mountain. This completes the 3 in that row, and greys out the mountain to the left. This then means the 4 is also the same mountain, and the whole mountain is covered in snow! Looking at the 6 and 7 clues in the columns, a few more snow cells can be deduced giving a couple more snowy peaks.

### 3. More progress:

Looking at the 4 clues top left, as the snow must be at the top, the bottoms of mountains taller than that clue size can be greyed out. As there are a few 2 clues, this is particularly useful.

### 4. A small sticking point:

The higher 5 clue on the left must be a 4 and a 1, so the 1 must be filled. This greys out the row above as the 6 in that column only has 1 more snow cell left. After this its hard to see what to do next. However, consider the aforementioned 5 clue. If it is not the 4 on the left, then all remaining cells in the 9 must b filled, but this would give a 7 in the 6 column. Hence it must be the leftmost 4. This completes the 7 column, and the 5 column.

### 5. Nearly done:

The 6 column is twinned with the 4, and hence a cell in the 6 column that's not in the 4 column can be greyed out. The 2s top left are also restricted. The grey in the 5 column greys out that row (somehow missed this earlier) leaving one solution for the 6 and 4.

### 6. Complete!

There is only 1 solution for the 2s top left!

• Yep, that's it! Great job, and nice write-up! Dec 30, 2021 at 15:00
• @JeremyDover lots of fun! Glad this concept was brought back up Dec 30, 2021 at 15:00