In short. Each number is the length of an unbroken run of filled squares in that row or column, and the numbers appear in the order the runs appear. Two runs are always separated by at least one empty square. The fastest way in is the overlap rule: in a line of length n, a run of length b always covers the middle 2b − n squares, wherever it sits. Mark those, and the grid starts to unfold.
What the numbers actually say
A nonogram — also called a griddler, hanjie, or japanese crossword — is a grid where a hidden picture is described entirely by numbers written along its top and left edges.
Read a line labelled 4 2. It says: somewhere along this line there is a run of exactly four filled squares, then later a run of exactly two, in that order, with at least one empty square between them. It does not say where. That is the whole puzzle.
Two consequences worth internalising early. First, a line labelled 0 is entirely empty — and that is real information, not a blank. Second, the minimum room a line needs is the sum of its numbers plus one gap between each pair: 4 2 needs 4 + 1 + 2 = 7 squares at the very least. If the line is only eight long, there is barely any slack — and slack is what you are always measuring.
The overlap rule opens almost every grid
This is the single technique worth learning first, and it does most of the work.
Take a line of 10 squares labelled 8. You do not know where the run of eight starts, but you can test the extremes. Pushed hard left it covers squares 1–8. Pushed hard right it covers 3–10. Whatever the truth, squares 3 to 8 are filled in both cases — so they are filled, full stop.
leftmost ████████·· rightmost ··████████ certain ··██████·· ← six squares proved, without knowing the answer
The arithmetic generalises: a run of length b in a line of length n guarantees 2b − n squares in the middle. If that number is zero or less, the run tells you nothing yet — which is exactly why big numbers are your friends and you should always start with the fullest lines on the board.
The same reasoning works with several runs: compute the leftmost possible arrangement of all of them, then the rightmost, and keep whatever agrees.
Crosses carry half the reasoning
Beginners fill squares and leave the rest blank. That throws away half of what they have worked out, because an empty square you have proved empty is worth exactly as much as a filled one — and the next deduction usually depends on it.
Mark them. A crossed square is a wall, and walls are what turn a vague line into a short one. A line of 10 with a cross at square 6 is really two independent lines of 5 and 4, each far easier to reason about than the original.
Work from the edges
Edges give free certainty, because a run at the border has nowhere to slide.
- If the first square of a line is filled and the line starts with 3, then squares 1, 2 and 3 are filled and square 4 is empty. No ambiguity at all.
- If the first square is crossed, the whole line shifts by one and you can redo the overlap arithmetic on a shorter line.
- A filled square adjacent to a cross behaves like an edge — which is why marking crosses keeps paying you back.
Know when a line is finished
When the filled squares in a line already account for every number, everything else in that line is empty — cross the whole remainder at once. It feels like bookkeeping, but each of those crosses is a wall for the crossing lines, and that is usually where the next deduction comes from.
The reverse check is just as useful: if the empty squares already leave exactly enough room for the numbers, the remaining squares must all be filled.
You should never have to guess
This is the line between a good nonogram and a bad one, and it is worth being blunt about.
A properly built puzzle can be solved by pure deduction: at every stage, some line has something new to prove, and you can reach the finished picture without ever trying a square to see what happens. A puzzle that stalls — where nothing anywhere is provable and the only way forward is to pick a square and hope — is not hard, it is broken. It has usually got there by having more than one valid solution.
So if you are stuck, the answer is almost never to gamble. It is that some line still has a deduction in it you have not read. Sweep the fullest rows and columns again, and pay particular attention to lines you have already partly solved: those are the ones whose walls have moved since you last looked.
Getting faster
- Start with the biggest numbers. The overlap rule pays proportionally to run length.
- Re-read a line whenever a crossing line changes it. Most missed deductions are old lines with new walls.
- Cross as you go. It is not tidying, it is reasoning.
- Count before you fill. On a tight line, one mental subtraction beats three corrections.
- Do not solve the picture. Guessing the subject then filling squares to match is how mistakes get in — the numbers are the only evidence.
Where to practise
Nono is a free nonogram game you can play in a browser, on phone or desktop, with no download and no account. Boards run from a gentle 5×5 up to 15×15, and every single one has been checked by a solver before shipping: if it cannot be cracked by pure deduction, it does not appear in the game. Solve a grid and it colours itself in to reveal the picture.