To solve a Nonogram, work one line at a time: for each row or column, find the squares that are filled, or empty, however its blocks end up sitting. Each square you settle tells the line running the other way something new, and the puzzle unravels from there. Six techniques cover it, from finding overlaps on an empty grid to listing the ways a line can still be filled.
New to Nonograms? Read the Nonogram rules first. This page assumes you know that a clue lists runs of filled squares in order, with at least one empty square between runs.
The idea behind all of them: pack left, pack right
Almost every technique starts the same way. Push all the blocks in a line as far left as they’ll go, then as far right. Where a block sits in between, it can’t be further left than its left packing, or further right than its right packing. Squares it covers both times are filled; squares no block can reach are empty.
When you pack, crossed-out squares get in the way: a block can’t sit on one, so it moves past it. That’s why crosses matter so much.
1. Finished lines
When a line’s filled squares already match its clue, every other square in it is empty. Cross them all out straight away. Those crosses are what the crossing lines need.
2. Overlap
Pack left, pack right, and fill the squares a block covers both times. On an empty grid this only works for clues that are big for their line. The slack rule tells you which: any block longer than the line’s slack has filled squares.
Overlap keeps working as the grid fills up. Crossed-out squares push blocks further in, so a line with crosses can overlap even when its empty version doesn’t.
3. Edges
A filled square close to the start of a line must belong to the first block. That block can’t start before the edge (or before the first square that isn’t crossed out), so it has to reach past the filled square. The same works from the other end, with the last block.
4. Out of reach
Pack left and pack right again, and look for squares that no block can reach in either packing, or anywhere in between. They’re empty.
5. Small gaps
A stretch of open squares between two crosses (or a cross and the edge), with nothing filled in it, that’s shorter than the smallest block in the clue can’t hold any block. Cross it out.
6. Every arrangement
When none of the quick techniques find anything, pick a line that’s mostly settled and list every way its blocks could still fit. A square that’s the same in all of them is settled. It’s slower, but it always finds what one line can tell you. The worked example below shows it in action.
How much each technique does
We solved 100 puzzles of each size from the game’s generator by following the hints, which always use the simplest technique that works. This is how many times each technique was used, on average, per puzzle:
| Technique | 5×5 | 10×10 | 15×15 |
|---|---|---|---|
| Overlap | 7.7 | 21.8 | 41.8 |
| Finished lines | 6.0 | 15.5 | 24.4 |
| Edges | 0.1 | 1.3 | 8.4 |
| Out of reach | 0.0 | 0.8 | 4.3 |
| Small gaps | 0.0 | 0.0 | 0.3 |
| Every arrangement | 0.1 | 0.6 | 6.0 |
Overlap and finished lines do most of the work at every size. The others matter more as the grid grows. Every arrangement was needed in 7 of the 100 5×5 puzzles, 22 of the 10×10s and 70 of the 15×15s. So on a big puzzle, expect to list a few lines out by hand.
A 10×10, solved in three stages
This puzzle comes from the game’s 10×10 size.
Stage 1: sweep for overlaps
Before filling anything, check every line for an overlap. Six of them have one: rows 5 (6) and 6 (7), and columns 5 (8), 6 (10), 7 (9) and 8 (6). Column 6 is completely full. Between them they fill 27 squares.
Stage 2: work back and forth
Now take each line that’s just changed and look at it again. Seven steps follow: four finished lines, one overlap, one edge and one out-of-reach. Then the quick techniques run dry. Nothing on any line can be settled by them.
Row 2’s clue is 1 2. Squares 6 and 7 are filled, and squares 4 and 8 are crossed out. List the ways 1 2 can still fit:
The filled pair can only be the 2 (a 1 can’t cover two squares), so the single square has to come before it, somewhere in squares 1 to 3. In all three arrangements, squares 5, 9 and 10 are empty, so cross them out. That’s what the quick techniques couldn’t see: they don’t know which block the filled pair belongs to.
Stage 3: finish with the quick techniques
Those three crosses are enough. Nine more overlaps and eleven finished lines complete the picture, without needing to list any more arrangements.
When you get stuck
- Look at the lines that just changed. Every new square changes two lines, and the next move is usually on one of them.
- Cross out as you go. A filled-in line with its empty squares left blank gives the crossing lines nothing.
- Go back to the long clues. A line that didn’t overlap at the start may now, if crosses have pushed its blocks inward.
- List the arrangements on a nearly finished line. With only a few unknown squares, there are only a few ways to fill them.
- Don’t guess. Every puzzle here can be finished one line at a time.