KNS Puzzles offers the Skyscrapers puzzles in the following formats:
4 x 4 - Level 1 - Level 2
5 x 5 - Level 1 - Level 2 - Level 3
6 x 6 - Level 1 - Level 2 - Level 3
7 x 7 - Level 1 - Level 2 - Level 3
8 x 8 - Level 1 - Level 2 - Level 3
9 x 9 - Level 1
Complete the grid such that every row and column contains the numbers 1 to the size of the grid. Each row and column contains each number only once. The clues around the outside tell you how many skyscrapers you can see. You can't see a shorter skyscraper behind a taller one. What are the numbers around the edges? Imagine standing around the edge, these numbers tell you how many skyscrapers you can see. You might be able to see any number from 1 up to the size of the grid.
Here are a few examples of how the clues help us to see which skyscrapers we might be able to see:
This is the start of the puzzle.
The 4 clue tells us that we can see all 4 skyscrapers, so they must be in order of size.
The 1 clue tells us that we can see only one skyscraper, which must be the <4>.
The 3 clue tells us that we can see three skyscrapers, which means that the <4> can't be first or second, and in fact the remaining <1>, <2>, <4> must be in order of size.
The 2 clue tells us that the first square can't be a <1> (otherwise we'd see 4 skyscrapers), so the first square must be the <3>.
This is the only square for the <3> from Column 3.
The <1> from Row 2 can't go in the last square as we already have a <1> in the end column, so this square must be the <1>.
The puzzle now completes using the technique from Step 6.
If you decide that a particular square could be two (or more) different numbers, you can enter them.
Once you have pencil marks these can be used for some advanced thinking. For example, the highlighted squares cannot contain a <4> otherwise the we could never see correct number of skyscrapers.