How to solve nonograms without guessing

A nonogram (also called Picross, Griddlers, Hanjie or paint-by-numbers) gives you numbers on each row and column: the lengths of the filled blocks, in order, with at least one empty cell between blocks. Paint the right cells and a picture appears. Every Pixel puzzle on DailyLogic is verified by a logic solver, so the techniques below are always enough; you never have to guess.

1. Overlap: the first cells you can fill

Take a 10-wide line with clue 7. Push the block to the far left (cells 1–7) and to the far right (cells 4–10). The cells covered in both positions, 4–7, are filled no matter where the block really is. In general, for a single block of length b in a line of length n, the middle 2b − n cells are certain whenever b > n/2.

With several clues, do the same after packing all blocks left and all blocks right; each block’s overlap is filled.

2. Lines that are completely determined

If the clues plus the mandatory gaps fill the whole line, there is only one arrangement. In a 10-wide line, 3 2 3 needs 3 + 1 + 2 + 1 + 3 = 10 cells: paint it entirely and ✕ the two gaps. A clue of 0 (or no clue) means the whole line is empty: ✕ it immediately.

3. Edges and known cells

If the first cell of a line is filled and the first clue is 4, cells 1–4 are filled and cell 5 is ✕. If a filled cell sits near the edge and the first clue is large, extend it: a filled cell 2 with clue 5 means cells 2–5 are filled (the block cannot start before cell 1 and must include cell 2).

4. Mark ✕ generously

Knowing where a block cannot be is as useful as knowing where it is. After completing a block, ✕ both ends. If the remaining unknown cells in a line are shorter than the remaining clue, ✕ them. In Pixel, right-click or a second tap marks ✕, and a clue fades when its blocks are complete.

5. Cross lines

Every cell you fill or ✕ from a row is new information for a column, and vice versa. Alternate between rows and columns; the puzzle “unzips” faster than working one direction at a time. If you are stuck, look for the line with the fewest remaining unknown cells.

Sizes

• 5×5: overlap and edges finish it in under a minute.
• 10×10: the daily size; mostly overlap, then crossing.
• 15×15: needs careful ✕ marking and the “remaining space” argument. Try Pixel Unlimited.

Related puzzles

Digits (mini sudoku), Regions (star battle), Duo (binary) and Trail (path) are the other daily logic puzzles on DailyLogic.