THE IDEA: TOWERS YOU LOOK ALONG
Picture each number in the grid as a building that many storeys tall. A 4 is a tall tower; a 1 is a little bungalow. Now stand at the edge of a row and look along it. A taller tower hides every shorter one behind it — so from where you stand you only count the ones that poke above everything in front. That count is what the edge clue tells you.
There are just two rules:
- Fill each row and column with 1 to 4, once each. (Bigger grids go 1 to 5, 1 to 6, and so on.) No repeats in a row, no repeats in a column — same as Sudoku, minus the boxes.
- Match every edge clue. The number outside a row or column says how many towers are visible looking inward from that side — counting only the ones not hidden behind a taller tower closer to you.
That's the whole game. And two edge clues are so generous they basically gift you a square — let's grab both.
LET'S ACTUALLY SOLVE ONE — STEP BY STEP
Here's a real Skyscraper. The grid's nearly empty; the numbers around the border are the view-counts. Don't try to read it all at once — we only ever look at one edge clue at a time.
The starting grid — a few givens, and view-count clues around every edge.
Step 1 — a clue of 1 is the best gift on the board.
Look at the 1 on the left of the top row. A clue of 1 means you can see exactly one tower looking in from that side. The only way that happens is if the very first building is so tall it hides every other — so the nearest cell has to be the tallest height, 4. Done, no scanning. A clue of 1 always plants the maximum right against that edge.
Step 2 — a clue equal to the grid size is just as kind.
Now the 4 above the third column. On a 4×4, a clue of 4 means you can see all four towers — and the only way nothing hides anything is if they climb in perfect order: 1, 2, 3, 4 going inward. So the nearest cell must be the shortest, 1. The two extremes — clue 1 → tallest first, clue 4 → shortest first — are the moves to hunt for every single time.
Step 3 — from here it's just a Latin square.
Two free squares already cracked the top row open. It holds a 4 and a 1, so the two gaps can only be 2 and 3 — and the no-repeats rule down the columns says which goes where. No edge clue needed: once a couple of towers land, plain Sudoku-style logic carries the rest.
That's the Skyscraper-specific bit, and it's most of the early game: grab the gift clues (1s and the full-size ones), drop their forced towers, then let no-repeats ripple outward. Every height you place rules itself out of its row and column, so the grid fills faster than you'd think:
Two-thirds there — each new tower forces the next, the clues and the no-repeats rule taking turns.
Done. Stand at any edge, count the towers you can see — it matches the clue every time. 👻
WHEN NO EDGE CLUE IS THAT OBVIOUS — TWO MORE TRICKS
The 1s and full-size clues are the freebies. When they run out, these two keep you moving — still no guessing.
1. A clue of 2 keeps the tallest away from the edge.
A middling clue still narrows things. If a side sees 2 towers, the nearest cell can't be the tallest (that would hide everything and show just 1) and it can't be so short that three or four peek over it. Often that's enough to say "this square is a 2 or a 3, nothing else" — and that's the crack its row needs. The bigger the clue, the earlier the tall towers have to appear.
2. Fall back on plain "what's missing?"
Underneath the view-counts it's just a Latin square — every row and column needs each height once. So whenever a row or column has a single empty square, the answer is simply whichever number it's missing. The edge clues open the door; the no-repeats rule walks you through the rest of the house.
So the whole loop is: take the gift clues (1 → tallest, full-size → shortest), squeeze the middling clues down to "one of these," and let no-repeats finish. Never a guess — every tower has a reason to be exactly that tall.
THAT'S IT — GO DO ONE
Read the edge clues, grab the freebies, drop the forced towers, let no-repeats mop up. The first time a lonely 1 on the border tells you exactly where the tallest tower stands, it feels a bit like the puzzle is on your side — because it is. No words, no maths homework, no ads in the middle of your puzzle — just you, a skyline, and a ghost who's quietly chuffed when the last tower lands.