How to solve nonograms
A nonogram is a grid with number clues beside each row and above each column. The clues list the runs of shaded squares in that line, in order, with a gap between runs. Solve it line by line: shade what is shaded in every possible placement, cross out what never is, and repeat until a picture appears.
The rules
- The numbers beside a row, or above a column, are the lengths of its shaded runs, in order from left to right or top to bottom.
- Runs in the same line are separated by at least one empty square.
- A line with the clue 0 has no shaded squares.
Nothing else. The finished grid is a small picture, but you never need to guess what it shows; the clues decide every square.
The overlap move
Slide a run as far left as it can go, then as far right. The squares it covers in both positions are shaded wherever it really sits.
With a 7 in a row of 10, the run covers squares 1 to 7 at the left and 4 to 10 at the right, so squares 4 to 7 are shaded for sure. A useful shortcut: a run longer than half the line always shades its middle. The move also works with several clues: push them all left, then all right, and compare each run with itself.
Cross out what can never be shaded
When a run is fixed, the squares on both sides of it are empty. When every run of a line is placed, the rest of the line is empty. Mark those squares with a dot or a cross; they are information too, and the columns that cross them will use it.
Line by line: a small one, solved
This nonogram is 5 squares wide and 6 tall:
- Row 4 has the clue 5 in a line of 5, so the whole row is shaded.
- Row 3 has 1 1 1. Three runs and two gaps need exactly 5 squares, so the row is fixed: shaded, empty, shaded, empty, shaded.
- Column 3 has 1 2 1 in a line of 6. Again the runs and gaps fill the line exactly: shaded, empty, shaded, shaded, empty, shaded.
Those three lines are settled before you think about anything else, and every other line now has squares to work from. Go round the rows and columns, applying the overlap move and crossing out, until the picture is complete: a small lantern.
Tips
- Start with the lines whose clues nearly fill them; add the clues plus the gaps and compare with the length.
- After every change, revisit the lines that cross it.
- Count gaps as well as runs: on a line of 15 with the clues 7 and 6, the runs and one gap need 14 squares, so almost everything is decided.
- Never shade a square because the picture "looks like" it needs one. The clues decide.
The same habit, in light
Nonograms train you to ask where a run can and cannot be. Light Up asks the same of a lantern: where can a lantern still stand, and which square can only be lit from one place? Nightwatch has a new Light Up board every night, free in your browser.
Nightwatch is on Android. On iPhone, play tonight's board here.
Free on Android. A one-time purchase stops every ad.
Questions
How do you solve a nonogram?
Work one line at a time. For each row and column, find the squares that are shaded in every possible placement of its runs and shade them, and find the squares that are empty in every placement and cross them out. Each change gives the crossing lines new information. Repeat until the grid is full.
What do the numbers in a nonogram mean?
They are the lengths of the runs of shaded squares in that row or column, in order. A row with the clue 3 1 has a run of three shaded squares, then at least one gap, then a single shaded square.
Can a nonogram have more than one solution?
A badly made one can. A good nonogram has exactly one solution that line-by-line logic reaches without guessing, like the small lantern on this page.
What is the overlap rule in nonograms?
Place a run as far to one side as it can go and then as far to the other side. The squares it covers both times must be shaded. A run longer than half of its line always shades its middle.