Nonogram solving techniques
Nonogram solving uses line logic. You study one row or column at a time and mark any cell that must be filled or empty. This guide names each technique, from simple overlap to full line logic, with a short example for each.
Updated 9 September 2026
01Simple boxes
Use this technique first, when a block almost fills its line.
Push the block as far left as it will go. Then push it as far right as it will go. Mark any cell that is filled in both positions, as the Wikipedia article on Nonograms describes for simple boxes. Those cells are the overlap and must be filled.
02Simple spaces
Use this technique after simple boxes, once you know at least one filled cell in the line.
List every valid position for the remaining blocks, given what you already know. Find any cell that stays empty in all of those positions. Mark that cell with X, as the Wikipedia article on Nonograms describes for simple spaces.
03Forcing
Use this technique when an X mark sits close to a block and leaves it little room to move.
An X near one end of the line pushes every remaining block toward the other end. The X narrows the space each block can occupy. Find the overlap inside that narrower space. Mark those cells as filled, as the Wikipedia article on Nonograms describes for forcing.
04Glue
Use this technique when a filled cell touches the border of the line.
A block that touches the border can only start at the border. Once you know the block starts there, you know every cell it covers. The Wikipedia article on Nonograms describes this rule as glue. Mark those cells as filled.
05Joining and splitting
Use this technique when two separate filled groups might belong to the same block.
Check how many blocks the clue allows between two filled groups. If only one block fits both groups, join them by filling the cells between them. If two blocks fit, a space must split the groups apart instead. The Wikipedia article on Nonograms describes both cases.
06Punctuating
Use this technique once a run of filled cells already matches its block length exactly.
A block cannot grow past the length given in its clue. When a run of filled cells already equals that length, mark X on both sides right away. The Wikipedia article on Nonograms describes this rule as punctuating. The two X marks seal the block and help you solve nearby cells.
07Mercury
Use this technique when a filled cell sits one cell past where a block touching the border would end.
Picture the first block starting right at the border. If a known filled cell sits just past where that block would end, the block cannot start at the border. Mark the border cell with X, as the Wikipedia article on Nonograms describes for this special case, called mercury.
08Edge logic
Use this technique when you want to test whether the first or last cell of a line can be filled.
Assume the edge cell is filled. Then check if the rest of the line can still match every known fact. If that assumption breaks a known fact, the edge cell must be empty instead. This check only looks at the edge, so it is faster than a full guess anywhere in the line.
09Full line logic
Use this technique when the named shortcuts above find nothing new.
List every valid placement of all blocks that still fits the known cells. Compare those placements cell by cell. Mark a cell as filled when every placement fills it, and mark it empty when every placement leaves it empty. The puzzle engine on this site uses this exact method on every line, with no named shortcut needed.
10Contradiction
Use this technique only when every other technique, including full line logic, finds nothing new anywhere in the grid.
Guess a value for one cell and solve as far as you can from that guess. If the guess leads to a broken line somewhere in the grid, the opposite value must be correct. If the guess never breaks anything, you learn nothing and must try a different cell. The puzzles on this site never need this step, because the generator only keeps puzzles that are line-solvable without it.
The order to try things
Start with simple boxes and simple spaces on every line. These two techniques are fast and often solve easy puzzles alone.
Next, look for edges and known cells that trigger forcing, glue, mercury and edge logic. These techniques use one known fact to solve nearby cells.
Use joining and splitting, and punctuating, to clean up blocks you have already found. Both techniques turn partial progress into finished blocks and fresh X marks.
If a line still has unknown cells, fall back to full line logic. This method checks every valid placement and finds any deduction the shortcuts missed.
Contradiction comes last, and only a puzzle that is not line-solvable ever needs it. The generator on this site never creates one of those.
When a puzzle needs a guess
A puzzle needs a guess only when line logic runs out on every row and column at once. Jan Wolter's survey on webpbn.com found that 81.8 percent of the hand-made puzzles in that database are line-solvable. The same survey found that only 0.4 percent of randomly generated puzzles are line-solvable.
Hand-drawn puzzles are far easier to solve without guessing than random grids, according to that survey. A human designer tends to leave enough clues for line logic to work all the way through.
Every puzzle this site generates passes a line-solvable check before it is shown to a player. If a generated grid needs a guess, the generator discards it and tries a new one.
Practice
Try the solver to test any set of clues without playing a full puzzle. Paste in your own clues and see each step explained.
Play a 5 by 5 puzzle to try these techniques on a small, quick grid. Read the rules page first if you are new to nonograms.
Frequently asked questions
Which technique should I learn first?
Start with simple boxes. The technique only needs one clue and finds cells that must be filled without checking anything else on the board. Simple spaces is a natural second step, since it uses the same overlap idea to find empty cells instead.
What is the difference between simple boxes and simple spaces?
Simple boxes finds cells that must be filled, using the overlap between the leftmost and rightmost position of a block. Simple spaces finds cells that must stay empty, using the same two extreme positions. Both techniques compare a block pushed to each end of the line.
Do I ever need to guess on this site?
Every puzzle on this site is line-solvable, so a guess is never required. The generator checks each new grid and keeps only the puzzles a player can solve with clues and logic alone. Jan Wolter's survey on webpbn.com shows that hand-made puzzles reach this level far more often than random ones.
What is full line logic?
Full line logic checks every valid placement of the blocks in a line against what is already known. A cell that is filled in every valid placement gets marked as filled. A cell that is empty in every valid placement gets marked with X. The method finds everything a single line can reveal, even without a named shortcut rule.
Why is a technique called mercury?
Mercury is the name the Wikipedia article on Nonograms uses for a special case of simple spaces. The technique applies when a filled cell sits just past where a block touching the border would end. That filled cell proves the block cannot start at the border, so the border cell must be empty.