How to solve nonograms: Picross tips, tricks and worked examples

01What a nonogram is, in one minute

A nonogram is a grid with number clues beside every row and above every column. Each number is the length of a run of filled squares in that line, and the runs appear in the order the numbers are written, with at least one empty square between neighbours. Fill the grid so that every line matches its clue and a pixel picture appears. If you want to try one while you read, play nonograms online free, starting with a 5x5.

The same puzzle is sold under other names: Picross (Nintendo's name), Griddlers (a British newspaper name), Hanjie, paint by numbers, Japanese crossword. In French it is a nonogramme, in German a Nonogramm, in Dutch a Japanse puzzel, in Spanish a nonograma. The rules are identical everywhere.

02How to read a clue and measure its slack

Take the clue 3 1 in a line of 8 squares. The two blocks need 3 + 1 = 4 filled squares and one gap between them, so 5 squares at the very least. The line has 8, so 3 squares of slack are left to move things around. Slack is the most useful number in nonograms: the smaller it is, the more you already know about the line.

Slack = line length minus (sum of the clue numbers plus one gap for each pair of neighbouring numbers). Slack 0 means the line is fully decided. A slack smaller than a block means that block overlaps with itself wherever you slide it, and the overlap squares are certain. A slack as large as the block gives nothing yet.

03The overlap trick with real numbers

Imagine a row of 10 squares with the clue 7. Push the block as far left as it goes and it covers squares 1 to 7. Push it as far right and it covers squares 4 to 10. Squares 4 to 7 are covered both ways, so they are filled for certain. The rest is open for now.

Now the clue 3 2 1 in 10 squares. The blocks and gaps need 3 + 2 + 1 + 2 = 8 squares, so the slack is 2. The 3-block is bigger than the slack by exactly one: leftmost it covers squares 1 to 3 and rightmost it covers squares 3 to 5, so square 3 is filled. The 2-block (leftmost squares 5 and 6, rightmost squares 7 and 8) and the 1-block have a slack as big as they are, so they give nothing yet. That single certain square is enough to start crossing lines.

• Slack 0: the whole line is decided, including the gaps.
• Slack smaller than the biggest block: that block has certain squares in the middle.
• Block bigger than the slack by n: n squares of that block are certain.

04Edges, splitting and simple spaces

Edges: as soon as a filled square is at the very edge of a line (or next to a cross at the edge), the first block must start there. You can fill the whole first block and cross out the square right after it. The same works from the other end for the last block.

Simple spaces: if a gap between two crosses is shorter than the smallest block still to place, nothing fits there, so cross it out. This clears a surprising amount of clutter, and the new crosses often finish a block elsewhere.

Splitting: a cross in the middle of a long stretch splits it in two. Every remaining block has to fit entirely in one of the parts, so count which blocks can go where. If a part is too small for any block, cross it. If only one block can fit a part, it has to live there and you can look for overlaps inside it.

05Glue, joining and counting

Glue: when you know a filled square belongs to a certain block (for example it is the only place a 4-block can be reached), the block must extend from it by up to its full length. Fill squares until the block would run past what is possible.

Joining: two filled squares that must belong to the same block are joined with every square between them filled. Combine this with a cross at the end and you can often finish a block outright.

Counting: when the long blocks are placed, the leftover small blocks have only a few possible spots. Count the blocks that remain and the gaps they need. Squares that no block can still reach are empty, so cross them.

06A good order for solving a whole puzzle

Go through all rows once, then all columns once, applying whichever technique fits. Then go around again. After a couple of rounds the grid usually becomes dense enough that every line is nearly done. The puzzles on PlayNest are built so that this simple loop always finishes: each is checked by a line solver that proves a single solution reachable by logic alone, so you never need to guess.

Work in pen-like order: fill what is certain, and cross what is certain. Do not leave a square empty and unmarked when you actually know it is empty. A cross is information, and the next line you look at may need it.

• Round 1: list the lines with slack 0 and the big overlaps.
• Round 2: add edges and crosses from what you found.
• Round 3: use simple spaces and splitting on the busy areas.
• Round 4 onwards: count remaining blocks until the picture appears.

07Mistakes to avoid and how to recover

The most common mistake is filling a square because it feels likely. Nonograms never need that. If you cannot justify a square from one line alone, leave it and move on. A wrong fill early can ruin the grid ten minutes later, and finding it is painful.

If a line suddenly cannot be satisfied, there is a mistake somewhere in the crossing lines. In the game, switch on Check to mark wrong squares, or use Undo to walk back stroke by stroke. Hint finds a square that logic proves and shows which row or column it came from, which is a good way to see a technique you missed.

08Where to practise next

Start with 5x5 puzzles until the overlap trick feels natural, then try 10x10, which is the classic size. After that, 15x15 and 20x20 reward patience, and the Daily puzzle gives you one fresh picture every day. If you enjoy this style of reasoning, Minesweeper and Sudoku use the same habit of deducing one certain square at a time, and the Mahjong Solitaire strategy guide shows how planning ahead works in a different puzzle. For another game built on clue-reading, see how to win Mastermind with Knuth's algorithm.