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Skyscrapers

Place buildings of heights 1 to n, once per row and column, so the edge numbers count how many you see from each side. 4×4 up to 6×6.

  • Logic
  • Untimed
  • 9 levels

How it plays

Each cell holds a building of height 1 up to the size, each height once per row and column. A number on the edge counts how many buildings you see looking in from there: a taller building hides every shorter one behind it.

A 1 means the tallest stands against that edge; the size itself means the line rises one step at a time. Any clue c caps the first cell at n − c + 1, the next at one more, and so on.

Levels take edge clues away, then grow the city. Every puzzle has exactly one solution, checked by a solver.

Keys

Space starts and skips ahead · 1–9 pick · Enter submits · Esc stops. On a phone, tap.

What it trains

This practises reasoning about order and what hides what, alongside elimination. It is practice at these puzzles, not a measured gain in reasoning elsewhere.

Learn

How to get better at skyscrapers: the method, the techniques, what each new level asks of you, and the traps the wrong answers are made of.

Your approach to each question

  1. Scan the edge for the giveaways: a 1, and a clue equal to the size. Fill those lines first.
  2. Write in what every other clue rules out near its edge: the bigger the clue, the lower the heights allowed close to it.
  3. Find where the tallest building can stand in each row and column. It must be somewhere in every line, and every clue of 2 or more forbids it in the cell next to that edge.
  4. Then work like a sudoku: each height once per row and column. A height with only one possible cell in a line goes there.
  5. Before you submit, check each clue by looking along its line from the edge and counting the buildings that are taller than all before them.

Techniques and tricks

  • A 1 means the tallest is in front

    A clue of 1 sees only one building, so the tallest, n, stands right against that edge.

  • A clue of n is a staircase

    Seeing every building means they rise one step at a time: 1, 2, 3 … n, starting from that edge.

  • Cap the cells near a clue

    With clue c, the nearest cell is at most n − c + 1, the next at most one more, and so on. A big clue keeps the tall buildings away from its edge.

    e.g. In a 5×5, a clue of 3 caps the nearest cell at 3 and the next at 4.

  • Opposite clues that add to n + 1

    If the clues at the two ends of a line add up to n + 1, the tallest building is fixed: it stands as many cells in from one end as that end’s clue.

    e.g. 5×5 row with 2 on the left and 4 on the right: 2 + 4 = 6, so the 5 is in the second cell from the left.

  • 1 opposite 2

    With a 1 at one end and a 2 at the other, the tallest is at the 1’s end and the second tallest at the 2’s end — the 2 sees it and then the tallest.

    e.g. 5×5: 1 on the left, 2 on the right gives 5 at the left end and 4 at the right end.

  • A 2 never has the tallest in front

    A clue of 2 sees the nearest building and then the tallest. So the nearest cell is not n, and every building between it and the tallest is shorter than it.

As the levels climb

  • The ladder is a fixed list of up to nine rungs, cut short by the “Largest city” setting: 4×4, then 5×5, then 6×6, and at each size the edge clues thin out from most of them to the fewest that still leave one answer.
  • As clues thin, the giveaway 1s and n’s get rarer. Lean on the caps and on where the tallest can go; when a line has no clues, it is filled by its crossing lines alone.
  • Now and then a few heights are printed in the grid, because even the full edge would not settle one city. Treat them as fixed: cross them out of their row and column first.
  • A 6×6 means six heights in every line, so the caps and the sudoku step both matter more. With “Time pressure” on, the clock gives a minute plus twelve seconds per open cell.

Traps to avoid

  • Counting every building: a clue counts only the ones you can see. A building hidden behind a taller one does not count, however tall it is.
  • Reading the clue from the wrong side: a number above a column looks down it, one on the right looks left along the row. Always count from the clue’s own edge.
  • Forgetting the opposite edge: a line has two clues. A placement that satisfies the left clue can break the right one.
  • Putting the tallest next to a 2: a 2 means at least one building is seen before the tallest, so n can never stand against a 2.

How to practise

  • Turn “Every edge clue shown” on while you learn the caps and opposite-clue moves; turn it off to make the thinning rungs count.
  • Set “Largest city” to 4 or 5 until you can finish without guessing, then let it run to 6.
  • After each city, pick one clue and recount it along its line. Seeing which buildings hide which is the core skill.

Levels

It is untimed unless you turn the clock on. There are 9 levels with the default settings, and the counter stops at the real top. Your level is judged on your last ten answers, every ten: 90% moves you up, below 80% moves you down, which holds most people near four in five right.

All of it is in the settings beside Start — how many answers a judgement looks at and how often it recalibrates, the thresholds, the time, which questions, how many options, and whether you see each verdict at once or review them together at the judgement. You can also jump to any level.

More logic

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