How to Solve Nonograms: A Step-by-Step Method
Nonograms, also known as picross or griddlers, are picture puzzles you solve with logic. Numbers beside each row and above each column describe the filled cells in that line. Work out every cell and a picture appears. They look intimidating at first, especially a 15x15 grid covered in numbers, but almost all of the reasoning comes down to a handful of simple ideas applied over and over.
This guide explains those ideas, then walks through a complete 5x5 puzzle one line at a time. You can practice everything here in our game Pixel Logic. It has 32 puzzles, and each one can be solved with the line-by-line reasoning described below, with no guessing.
What a clue actually says
A clue like 3 1 2 on a row means: somewhere in this row there is a block of 3 filled cells, then later a block of 1, then later a block of 2. The blocks appear in that order, from left to right (or top to bottom for columns). There is at least one empty cell between blocks, and there can be any number of empty cells before the first block, between blocks, and after the last.
Two special cases:
- A clue of
0means the line has no filled cells at all. - A clue equal to the line’s length means every cell is filled.
The whole game is about working out where each block can sit.
Technique 1: The minimum length check
Add up the clue numbers, then add one for each gap between blocks. That’s the shortest space the clue can fit in. For 3 1 2, it’s 3 + 1 + 2 + 2 gaps = 8.
If that minimum equals the line length, there’s only one arrangement, and you can fill the line immediately. In a 10-cell row, the clue 4 5 needs 4 + 5 + 1 = 10 cells, so the row is four filled, one empty, five filled.
The difference between the line length and the minimum is the line’s slack. A line with a slack of 0 is solved. A line with a small slack usually gives you a lot.
Technique 2: Overlap
This is the most important technique in nonograms. Take a single block and imagine pushing it as far left as it can go, then as far right as it can go. Any cell it covers in both positions must be filled.
For a single block, the rule of thumb is: if the block is longer than the slack, it fills (block − slack) cells in the middle. A block of 7 in a 10-cell row has a slack of 3, so the middle 7 − 3 = 4 cells are filled.
With multiple blocks, pack them all to the left, then all to the right, and compare where each block lands. A cell counts as certain only when the same block covers it in both arrangements.
Technique 3: Use the edges
A filled cell against the edge of the grid is gold. If the first clue in a row is 3 and the leftmost cell is filled, that cell must belong to the first block, and the block must start right there. The first three cells are filled and the fourth is empty.
The same idea works against any cell you’ve marked as empty. An empty cell acts like a wall, and a filled cell right next to a wall anchors a block.
Technique 4: Cross out what can’t be reached
Marking empty cells is half of the game. After a few fills, look at each line and ask which cells no block could possibly reach. If a row’s clue is 2 and you’ve found a filled cell in column 6, the block covers either columns 5–6 or 6–7. Everything else in the row is empty.
When every block in a line is accounted for, cross out all the remaining cells. Our game does this step for you, graying out the rest of a line as soon as its filled cells match the clue.
Technique 5: Swap between rows and columns
Every cell belongs to one row and one column. When you solve a cell in a row, you’ve given its column new information. The basic rhythm of nonogram solving is: sweep through the rows, then sweep through the columns, then back to the rows, until the picture is done. When you’re stuck, it’s almost always because a line changed and you haven’t looked at it again.
A worked example
Here’s a 5x5 puzzle. Rows are numbered 1–5 from the top, and columns are lettered A–E from the left.
| Clue | |
|---|---|
| Row 1 | 1 1 |
| Row 2 | 5 |
| Row 3 | 5 |
| Row 4 | 3 |
| Row 5 | 1 |
| Column A | 2 |
| Column B | 4 |
| Column C | 4 |
| Column D | 4 |
| Column E | 2 |
We’ll draw the grid with # for filled, x for empty and . for unknown.
Step 1: Full lines. Rows 2 and 3 have the clue 5 in a 5-cell line, so they’re completely filled.
A B C D E
1 . . . . .
2 # # # # #
3 # # # # #
4 . . . . .
5 . . . . .
Step 2: Overlap in the columns. Columns B, C and D each have a block of 4 in 5 cells. The slack is 1, so the middle 4 − 1 = 3 cells (rows 2, 3 and 4) are filled in each. Rows 2 and 3 are already done, so this adds row 4 in columns B, C and D.
A B C D E
1 . . . . .
2 # # # # #
3 # # # # #
4 . # # # .
5 . . . . .
Step 3: Finish row 4. Row 4’s clue is 3, and B, C and D already form a block of 3. The row is complete, so A4 and E4 are empty.
Step 4: Finish columns A and E. Column A’s clue is 2, and A2 and A3 are filled. That block is done, so A1, A4 and A5 are empty. Column E works exactly the same way.
A B C D E
1 x . . . x
2 # # # # #
3 # # # # #
4 x # # # x
5 x . . . x
Step 5: Row 1. Row 1 needs 1 1, but A1 and E1 are empty, so the clue has to fit into B, C and D. Two single blocks with a gap between them need exactly 3 cells, so there’s no slack. B1 is filled, C1 is empty, and D1 is filled.
Step 6: Back to the columns. Column B now has rows 1 through 4 filled. That’s its block of 4, so B5 is empty. Column D works the same way, so D5 is empty. Column C has an empty cell in row 1, so its block of 4 must be rows 2 through 5, and C5 is filled. That also satisfies row 5’s clue of 1.
A B C D E
1 x # x # x
2 # # # # #
3 # # # # #
4 x # # # x
5 x x # x x
It’s a heart. Every step used one line at a time, and nothing was guessed. Bigger puzzles work exactly the same way. There are just more lines to cycle through.
Tips for bigger grids
- Open with the largest clues. On a 15x15 grid, look for lines whose clue totals leave a small slack. Those give you overlap cells right away.
- Don’t forget small clues next to known cells. A
1next to a filled cell is often solved on the spot, and the cells around it can be crossed out. - Mark empties as confidently as fills. Crosses create the walls that anchor blocks against them.
- Keep track of which block is which. In a line with several blocks, the overlap and edge rules only work when you know which block a filled cell belongs to. Count from the nearest edge or wall.
- Recheck lines after every change. Solving a nonogram mostly means going back to lines you already looked at, now with one more known cell.
When you’re ready, start with the 5x5 set in Pixel Logic to get used to the rhythm. Then move up to 10x10, where overlap and edges do most of the work, and finish with the 15x15 pictures.