Solving techniques
The deduction methods experts use to crack hard grids — without ever guessing.
Once you know the rules, the difference between a solver who stalls on a hard puzzle and one who finishes it is a small set of repeatable deductions. None of them require luck. A well-constructed nonogram — including every puzzle on this site — has exactly one solution that is reachable by pure logic, so guessing is never required and never helps.
Each technique below has its own focused guide with illustrated, worked examples. They are ordered the way you will actually use them mid-solve: the opening sweeps first, the boundary tricks next, the line-level arithmetic and the what-if proof last. If you are new to the puzzle, read the beginner's guide first, and keep the glossary handy for unfamiliar terms.
Simple boxes (the overlap method)
The most productive opening move on any grid. When a run is long relative to its line, its leftmost and rightmost placements overlap, and every cell in the overlap is certainly filled.
Simple spaces (unreachable cells)
The mirror image of the overlap method: instead of asking which cells every placement covers, ask which cells no placement can reach, and cross them off.
Edge logic
The grid's edges are free information: the first clue is pinned against the left wall, the last against the right. A filled cell touching a wall resolves its whole run instantly.
Glue (anchored runs)
A filled cell near a wall 'glues' its run in place: wherever the run slides, it must keep covering that cell, which forces neighbouring cells to fill and distant cells to empty.
Splitting lines into segments
A single empty mark cuts a line in two. Ask which clues fit in which segment: runs too long for one side are forced onto the other, and each segment becomes a small line of its own.
Punctuating completed runs
The moment a run reaches its full length, the cells on either side of it are empty by definition. Sealing runs the instant they complete keeps the whole board flowing.
Joining forces (counting slack)
Add up a line's clues plus the mandatory gaps and compare against the line length. The difference — the slack — tells you exactly how much every run can move, before you fill a single cell.
The contradiction test
Tentatively assume a cell is filled (or empty), follow only the forced consequences, and watch for an impossibility. If the assumption breaks the line, the opposite state is proven.
How the techniques fit together
In practice a solve is a loop, not a checklist. Open with a sweep of simple boxes and simple spaces across every row and column, sealing anything you finish with punctuation. Every cell you resolve changes a crossing line, where edge logic, glue and splitting pick up the new information. When a line stalls, count its slack to see whether it is worth more attention, and save the contradiction test for the rare cell nothing else reaches.
No guessing, ever. A good nonogram has a unique solution reachable by logic alone. Every puzzle on this site is generated and validated to meet that bar, so if you are tempted to guess, there is a deduction you have not spotted yet — usually in a crossing line. Slow down, recount the slack, and it will appear.
Put these techniques to work.