How to Solve 10×10 Nonograms

What changes from 5×5

On a 5×5 board most clues nearly fill their line, so cells fall out almost at once. On 10×10, many clues leave room to slide, and you need to measure that room before you can place anything. The tool for that is slack.

Measure the slack of each line

Slack is the line length minus the space the clue needs: its numbers plus one gap between each pair. For a ten-cell line:

• Clue 3 2 3 needs 3 + 2 + 3 + 2 = 10 cells. Slack 0: the line is fully determined.
• Clue 4 4 needs 4 + 4 + 1 = 9 cells. Slack 1: each block has one cell of play, so three of its four cells are certain.
• Clue 6 needs 6 cells. Slack 4: the block is longer than the slack, so 6 − 4 = 2 cells in the middle are certain.
• Clue 2 2 needs 5 cells. Slack 5: no block is longer than the slack, so the clue alone proves nothing.

The rule: a block longer than the slack has (block − slack) guaranteed cells. The Nonogram overlap technique explains why.

Worked example: Petal

Petal is a 10×10 puzzle in the Bloom chapter of Spring Forest. Like every Spring Forest puzzle, it has exactly one solution and can be finished with line logic alone.

Step 1: take the zero-slack lines. Row 3 (3 2 3) and columns 4 and 7 (2 4 2) each need exactly ten cells, so they are complete straight away, × gaps included.

Step 2: take the overlap from long blocks. Columns 3 and 8 (4 4) have slack 1, which gives three certain cells per block. Rows 4 and 7 and columns 5 and 6, each a single 6, have slack 4, which gives their middle two cells.

The other clues (2 2, 3 3, 4, 2 2 2 and 1) all have a slack at least as large as their biggest block, so on a blank board they prove nothing. Leave those lines for later.

Step 3: work the crossings. Every new cell is information for the line that crosses it. Rows 4 and 7 now hold six filled cells in a row, which completes their 6, so the two cells at each end are ×. Rows 1 and 10 have filled cells in columns 4 and 7; each 2 must include one of them, so the two cells at each end are out of reach.

Step 4: repeat until the board is done. Keep alternating rows and columns, re-reading each line that changed. On Petal, that loop alone finishes the picture, with no guessing and no contradiction checks.

A 10×10 routine

1. Work out the slack of every line before filling anything.
2. Fill zero-slack lines completely, × gaps included.
3. Take the overlap from every block longer than its line's slack.
4. Mark finished lines and cells no block can reach.
5. Re-read every line that crosses a cell you just changed.
6. When nothing changes any more, use the ideas from the 15×15 guide; they work on 10×10 too.

Common 10×10 mistakes

• Starting with the small clues. A 1 or a 2 2 in a ten-cell line proves nothing on its own. Start where the slack is small.
• Counting the space wrong. A clue needs its numbers plus one gap between each pair, not the numbers alone.
• Not marking. On 10×10, × marks are what turn wide-open lines into lines with little slack.
• Forgetting to re-read. Most progress comes from lines that changed because a crossing line did.

Where to practise

Spring Forest has 14 puzzles at 10×10, Petal among them, and the Daily Nonogram is a new 10×10 every Tuesday, Wednesday and Thursday (UTC). For a quick warm-up, try the free 10×10 puzzle, no account needed. New to the rules? Start with how to play Nonograms.

Practise 10×10 in Spring Forest