Skyscrapers

The rules

Every cell holds a building with a height from 1 to N, where N is the size of the grid. As in sudoku, each row and each column contains every height exactly once.

The numbers around the edge tell you how many buildings can be seen from that point, looking along the row or column. A taller building hides every shorter one behind it. That makes a 1 easy to read: only the tallest building can be first in line on that side. A clue equal to N is just as generous, because the line must then climb 1, 2, 3 and onwards in single steps.

Sizes and levels

Easy grids are 4×4, medium 5×5, hard 6×6 and expert 7×7. Bigger grids keep fewer clues around the edge, and a few heights may be filled in from the start where the edge alone would not give a single answer.

Reading the clues

Start with the extremes. A 1 puts N next to that edge. An N fills the whole line. A 2 opposite a 1 tells you even more: N stands next to the 1, and the building at the end with the 2 must be the second tallest, N−1.

Next, use the rule that a clue of k means the tallest building is at least k−1 cells away from that edge, because k−1 shorter buildings have to be visible in front of it. In a 5×5 grid, a clue of 4 keeps the 5 out of the first three cells on that side.

Then look at opposite pairs. If the two clues on a line add up to N+1, every building on that line is visible from one side or the other. The tallest one then sits exactly at the position given by the near clue, and the heights rise towards it from both sides.

Once a few heights are fixed, the puzzle turns into a Latin square: each missing height in a row or column has only so many places left. Notes are useful here.

Controls

Tap a cell and choose a height, or type the number. Notes, undo, redo and hints work the same way as in the other number games. Edge clues are greyed out once their line is complete and correct.