Skyscrapers Puzzle

Skyscrapers: a Latin square you solve by sight lines

Fill the 5×5 grid with the heights 1 to 5 so no height repeats in any row or column. That part is a Latin square, and on its own it would be easy.

The numbers around the outside are what make it a puzzle. Each one tells you how many buildings you would see standing at that edge and looking down the row or column, where a taller building hides everything shorter behind it. A 1 means the nearest building is the 5, because nothing else can be seen past it. A 5 means the row climbs 1, 2, 3, 4, 5 in order — there is only one arrangement that shows five buildings, and finding a 5 on the edge is the luckiest thing that can happen to you.

The clue values and what they give you

• 1 — the 5 sits nearest that edge. One cell, solved.
• 5 — the entire line is determined, climbing 1, 2, 3, 4, 5 away from you, because that is the only order in which all five are visible.
• 4 — nearly determined. Work these immediately after the 1s and 5s.
• 2 — the 5 is second, or close to it. Useful in combination.
• 3 — the weakest clue a 5×5 grid can carry, and usually the last one you reach for.

Beginners tend to start at the top left. Better to scan the whole border for 1s and 5s first, place what those force, and only then work the middling clues against what is left.

What you can set

Two things: how many puzzles go on a page, from 1 to 6, and whether to append the solution page. The grid is fixed at 5×5.

That fixed size is a decision rather than a limitation. At 4×4 the edge clues barely constrain anything and the puzzles solve themselves; at 6×6 and above they get long rather than harder, and six of them will not fit on a page in any readable size. Five is where a Skyscrapers puzzle is a satisfying few minutes, which is what a page of six is for.

Solutions

Turn the toggle on and a separate page prints the completed grid for every puzzle on the sheet.

Where it fits

It suits a maths classroom better than most logic puzzles because the reasoning is explicit: you can say out loud why the 5 must sit at the front of a row clued 1, and a child can follow it. That makes it good for teaching deduction as a method rather than as a knack.

It also travels well. Six puzzles on one sheet, a pencil, and no need to explain the rules twice.

Puzzles are generated fresh every time. Print at 100% on A4 or US Letter.