Sum Skyscrapers: rules, tips and free puzzles online

Sum Skyscrapers works like Skyscrapers, but each clue is the total height of the towers you can see from that side, not how many there are. Play Sum Skyscrapers online free here, on grids from 5×5 to 7×7.

The tallest tower is always visible, so every clue is at least N. The art is working out which shorter towers make up the rest.

The rules

• The grid is N×N (5×5 to 7×7 here). Each row and column holds towers of height 1 to N, once each.
• A clue outside the grid is the sum of the heights of the towers visible from that side. A taller tower hides every shorter one behind it.
• Digits already in the grid are given clues.

How to start

Clue equal to N

If the clue is exactly N, only the tallest tower is visible, so N stands right at that edge.

The largest possible clue

If every tower is visible, they rise 1, 2, 3 and onwards, and the clue is 1 + 2 + … + N. On a 5×5 that is 15.

Subtract the tallest

Every clue includes N. Take N away and ask which shorter towers, rising from the edge, can make the rest. A 5×5 clue of 9 is 5 + 4 or 5 + 3 + 1, so the tower nearest the edge is 4 or 1. Then combine with row and column scanning from our solving techniques guide.

Common mistakes

• Counting towers instead of adding their heights.
• Forgetting that the tallest tower is always included in the total.
• Adding a tower that is hidden behind a taller one.

How the ranks scale difficulty

The same four ranks apply here as everywhere on the site. Lemma is a gentle warm-up, Proposition needs a real idea or two, Theorem is near-minimal with almost every clue load-bearing, and Conjecture is the sparsest of all, so expect to think hard.

Grids run from 5×5 at Lemma to 7×7 at Conjecture. Higher ranks remove more clues and givens.

There are 99,999 puzzles per rank, each with its own number, so you can replay one or share it. Every type also has a 30-puzzle collection that climbs from Lemma to Conjecture. Every puzzle is checked to have exactly one solution that you can reach by logic alone, with no guessing.

Keep exploring

• SkyscrapersEdge clues count the buildings you can see. Taller ones hide shorter.
• FutoshikiA Latin square with < and > signs between neighbouring cells.
• CalcudokuA Latin square with arithmetic cages: + − × ÷. Sizes 5×5 to 8×8.
• Solving techniquesSingles, pairs, cage arithmetic, line logic and Latin squares, all in one guide.
• All puzzle guidesEvery puzzle type on Hoot’s Puzzles, with rules and tips.