How to play Skyscrapers

Skyscrapers is a logic puzzle set in a tiny city. Every cell of the square grid holds a building, and each row and each column contains exactly one building of every height. The numbers around the edge are the clues: each one says how many buildings you would see looking along that row or column from that spot. A taller building hides every lower building behind it.

Every puzzle here is generated fresh by the game when you start it, has exactly one solution, and can be solved by reasoning alone. You never need to guess. The four levels grow from a 4x4 grid on Easy to a 7x7 grid on Crazy, and each level asks for deeper reasoning than the one before.

How to play on skill.games

When you open the game, the settings popup appears. Choose a level under DIFFICULTY, choose how mistakes are treated under MISTAKES, and press PLAY. A new puzzle is generated in a moment.

• The board takes up most of the screen: the grid in the middle and the clues in a band around it, one at each end of a row or column (not every end has a clue). Heights given at the start are printed in dark ink and can't be changed; the heights you enter appear in blue.
• Choosing a cell: tap any cell. Its row and column are shaded, the four clues that look along them are marked with a pale circle, and every cell holding the same height is highlighted.
• Entering a height: with a cell chosen, tap a number on the number pad (under the board, or beside it when your screen is wider than it is tall). The small number under each key shows how many of that height are still to place; a key fades out once every row has it.
• NOTES: tap NOTES to switch notes on. Numbers you tap are now pencilled into the cell as small candidates, and tapping one again removes it. Tap NOTES again to go back to entering heights. When you enter a height, it is removed automatically from the notes of every cell in its row and column.
• ERASE clears the chosen cell (its height or its notes).
• UNDO takes back your last action - a height, a note or an erase - all the way back to the start. Undo is free and unlimited.
• Highlighting a height: with no cell chosen, tap a number on the pad to highlight every cell and note holding it. Tap it again to clear the highlight.
• Finished lines: when a row or column is full and its clue is satisfied, the clue fades, so you can see at a glance which lines are done.

On a computer you can also use the keyboard: the arrow keys (or W, A, S, D) move between cells, the number keys enter a height, Shift and a number pencil a note, Backspace, Delete or 0 erase, N switches notes on and off, and Z undoes.

The top line shows the clock, the level, the grid size and your mistakes. The clock runs only while you play: it stops when the menu or a popup is open. The menu button in the top-left corner pauses the game, starts a new puzzle or switches the sound on or off. The game is saved after every move, so if you close the page you can press CONTINUE later and carry on with the same grid, notes, clock and undo history.

When the last cell is filled correctly, the board ripples and the results screen shows your time, your best time at that level (a star marks a new record), your mistakes, the grid size and the puzzle's code, together with your wins, losses, win rate and streaks.

Rules

The grid. On a grid of size N (4 to 7 here) every row and every column must end up holding each height from 1 to N exactly once.

Clues. A number at the end of a row or column says how many buildings are visible from there, looking along the line into the grid. A building is visible if it is taller than every building in front of it. The tallest building, N, is always visible and hides everything behind it. For example, the row 2 1 4 3 seen from the left shows 2 and 4 - two buildings; seen from the right it shows 3 and 4 - also two.

Givens. Some puzzles also start with a few heights already placed. They are part of the puzzle and can't be changed. Every puzzle has exactly one way to complete it.

Mistakes - Unlimited (the default). If you enter a height that is already in the same row or column, it turns red and the mistakes counter goes up by one. If you complete a row or column and a clue at its end counts a different number of buildings, the clue turns red inside a red ring and that also counts as a mistake. Nothing else is checked, so nothing about the solution is revealed. Because the solution is unique, a full grid with no red marks is always the right one.

Mistakes - 3 lives. Every height you enter is checked against the solution at once. A wrong height is marked in red and costs a life; the third mistake ends the game and counts as a loss. Undo can take a wrong height back, but not the life it cost.

Abandoned puzzles. Starting a new puzzle before finishing the current one counts as a loss in your statistics for that level.

Solving techniques

These are the methods the game's own solver uses to grade every puzzle, from the simplest up.

• Clue 1: only one building is seen, so the tallest one stands right next to the clue.
• Clue N: every building is seen, so the line rises 1, 2, 3 ... N away from the clue.
• How far in the tallest can stand: with clue k, at least k buildings must be seen before the tallest, so the tallest can't stand in the first k − 1 cells. More generally, the cell d steps in from clue k can be at most N − k + 1 + d tall.
• Singles: a height with only one possible place in a row or column, or a cell with only one possible height.
• Counting a line: when a row or column has only a few empty cells left, try the remaining heights in each order and keep the arrangements that match both clues. Whatever never appears in a cell can be crossed out. With three empty cells this is quick; with four or five it takes care; a whole line of six or more empty cells is expert work.
• Pairs and triples: two cells of a row that can only hold the same two heights claim them; the rest of the row loses those heights.
• X-Wing: a height confined to the same two columns in two rows can be removed from the rest of those columns.
• Advanced: XY-Wing, Swordfish, quads and simple colouring - longer "if this, then that" reasoning, still without guessing.

Strategy tips

• Start with 1s and Ns. A clue of 1 places the tallest building at once; a clue of N fills the whole line.
• Place the tallest buildings first. The tallest building in each line decides most of what is seen, and the distance rule rules out many cells for it.
• Read opposite clues together. A row with 2 on one end and 2 on the other can't have its tallest building at either end.
• Small clues mean tall buildings near the edge; big clues mean short ones.
• Use notes once the easy cells run out, then count the lines with the fewest empty cells.
• Don't guess. Every puzzle here can be solved by logic. If you feel stuck, there is a line you haven't counted yet.

Difficulty levels

The game generates every puzzle on the spot and grades it with a solver that works the way a person does, always using the easiest step available. A puzzle is given to you only if its hardest required step matches the level you chose.

• Easy: a 4x4 grid with at least 8 clues; the clue rules alone (1, N and how far in the tallest can stand) and singles are all you need.
• Normal: a 5x5 grid; at least one step needs counting a line with up to three empty cells, or a pair.
• Hard: a 6x6 grid; at least one step needs counting a line with four or five empty cells, a triple or an X-Wing.
• Crazy: a 7x7 grid; at least one step needs counting a whole line, an XY-Wing, a Swordfish, a quad or colouring.

Statistics and best times are kept separately for each level. If Skyscrapers is new to you, start on Easy: the 4x4 grids teach how the clues work.