Nonogram Techniques: Solving without Guessing
Every daily nonogram on this site can be solved by looking at one row or column at a time. These five techniques are different views of that one idea.
Last updated: September 28, 2026
The idea behind every technique
Imagine all arrangements of the groups that fit the clue and agree with the cells you already know. A cell that is filled in all of them is filled. A cell that is empty in all of them is empty. About the other cells nothing can be said yet.
The solver that tests the daily puzzles does exactly this for every row and column, again and again, until the grid is complete. The techniques below are quick ways to find the same cells without listing arrangements.
In the examples, # is a filled cell, x is a crossed cell and · is a blank cell.
Technique 1: overlap
Push all groups as far to the left as possible, then as far to the right as possible. Where the same group covers a cell in both positions, the cell is filled.
Example: a row of 10 cells with the clue 7. Pushed to the left, the group covers cells 1 to 7. Pushed to the right, it covers cells 4 to 10. Cells 4 to 7 are covered both times.
| Position | Cells 1 to 10 |
|---|---|
| Pushed left | #######··· |
| Pushed right | ···####### |
| Certain | ···####··· |
It must be the same group in both positions. If the first group pushed right overlaps the second group pushed left, that proves nothing.
Technique 2: counting the slack
The overlap can be calculated. Add the numbers of the clue and one gap for each pair of neighbouring groups. The difference between the length of the line and this sum is the slack: the distance the groups can slide.
Every group that is longer than the slack has certain cells: its length minus the slack. They are the last cells of the group when everything is pushed to the left.
Example: a row of 10 cells with the clue 3 4. The sum is 3 + 4 + 1 gap = 8, so the slack is 2. The group of 3 has 3 − 2 = 1 certain cell, and the group of 4 has 4 − 2 = 2.
| Position | Cells 1 to 10 |
|---|---|
| Pushed left | ###·####·· |
| Pushed right | ··###·#### |
| Certain | ··#···##·· |
If the slack is 0, the whole line is decided. If the slack is at least as large as the largest group, the line gives nothing at the start.
Technique 3: working from an edge
A filled cell near the edge of a line pins down the first group. If the first cell of a row is filled and the clue starts with 4, cells 1 to 4 are filled and cell 5 is crossed.
If the filled cell is not at the very edge, the group can still only slide a little. Example: a row of 5 cells, clue 2, cell 2 is filled. The group covers cells 1 and 2 or cells 2 and 3. Cells 4 and 5 are out of reach: cross them.
| State | Cells 1 to 5 |
|---|---|
| Before | ·#··· |
| After | ·#·xx |
Technique 4: crossing out
When the filled groups of a line have the lengths of its clue, every other cell of the line is empty. On this site the clue is then struck through. Cross the remaining cells, because these crosses are the information the other direction needs.
A finished group in an unfinished line also gives crosses: the cells directly before and after it are empty.
A crossed cell at the edge shortens the line. Example: a row of 6 cells with the clue 3, whose first cell is crossed. The group has to fit into cells 2 to 6. Pushed left it covers cells 2 to 4, pushed right cells 4 to 6, so cell 4 is filled.
Technique 5: splitting a line
Crosses in the middle divide a line into pieces. A piece that is shorter than a group cannot hold that group. If a piece is too short for every group that could reach it, cross the whole piece.
Example: a row of 9 cells with the clue 4, whose fifth cell is crossed. Both pieces, cells 1 to 4 and cells 6 to 9, have room for the group, so nothing is certain yet. If cell 8 becomes crossed as well, the right side has pieces of 2 and 1 cells only. The group is on the left: fill cells 1 to 4.
A routine that works
- Calculate the slack of every row and column. Fill the certain cells of the lines with little slack.
- Look at the lines that cross the new filled cells. Use the edge technique on groups near a border.
- Cross out finished lines and the cells next to finished groups.
- Repeat the overlap on lines that have become shorter through crosses.
- Change between rows and columns often. Every new mark in a row is news for a column.
Common mistakes
- Overlapping different groups. Count which group covers the cell in both extreme positions.
- Forgetting the gaps in the sum. Three groups have two gaps.
- Filling what is probable. A cell that is filled in most arrangements is still blank until it is filled in all of them.
- Leaving known empty cells blank. Without crosses, shortened lines and split lines stay invisible.
- Assigning a filled cell to the wrong group. In a line with several groups, first ask which groups can reach the cell at all.
Frequently asked questions
- Are these techniques really enough for every daily puzzle?
- Yes, together with the idea behind them: when none of the five shortcuts applies to a line, compare all arrangements of that line directly. That is exactly what the solver does, and a puzzle is published only if it finishes that way.
- What if no line gives a certain cell?
- In the daily puzzles this does not happen. Look again for lines that were shortened by crosses, and check that finished lines are crossed out.
- Are there techniques that use two lines at once?
- Yes, some nonograms elsewhere need reasoning over several lines or trial and error. The daily puzzles here are chosen so that they never need it.
- Where should I start in a 15 × 15 puzzle?
- With the lines of smallest slack. In a line of 15 cells a single group of 8 or more has certain cells. With several groups, calculate the slack: every group that is longer than the slack has certain cells.