Nonogram solving techniques

Simple boxestier 1

When: A block longer than half of the free room always covers the middle cells.

Slide a long block from one end of its free room to the other: the cells it covers in both positions are filled. With several blocks, do the same for each block, packed to the left and then to the right.

From one of our puzzles (10x10): In row 2 (clue 5 2), the blocks overlap themselves however they sit in the free room: C2-E2 are filled.

Practise it: Nonogram puzzles at Easy

Finished linestier 1

When: Once a line has all its filled cells, the rest of it is empty.

When a line has as many filled cells as its clue adds up to, every other cell in it is empty. Crossing them out gives the crossing lines room to work.

From one of our puzzles (10x10): Column H (clue 0) already has all its filled cells, so H1-H10 are empty.

Practise it: Nonogram puzzles at Easy

Spaces split the linetier 2

When: Crossed cells cut a line into pieces; count which blocks fit in which piece.

Crossed cells cut a line into pieces, and a block cannot jump over a cross. Count which blocks can still fit in which piece, then overlap them inside their piece.

From one of our puzzles (10x10): In row 1 (clue 4), the crossed cells decide which blocks fit in which gap: D1 is filled and I1-J1 are empty.

Practise it: Nonogram puzzles at Medium

Simple spacestier 2

When: Cells that no block can reach are empty.

Some cells are out of every block's reach once the crosses are taken into account: they are empty. This often clears the ends of a line.

From one of our puzzles (10x10): In row 1 (clue 4), the crossed cells decide which blocks fit in which gap: A1 is empty.

Practise it: Nonogram puzzles at Hard

Forcing from known cellstier 3

When: A filled cell near an edge or a space pins a block in place.

Filled cells pin blocks down. If the third cell from the edge is filled and the first clue is 4, that block must cover it, so it sits at cells 1-4, 2-5 or 3-6: every placement covers cells 3 and 4, so cell 4 is filled too.

From one of our puzzles (15x15): In row 10 (clue 1 3 1 3 1), the filled cells already known pin the blocks: in the leftmost and the rightmost placement alike, D10, L10 are filled and G10, I10 are empty.

Practise it: Nonogram puzzles at Hard

Out of reachtier 3

When: With the filled cells counted, some cells are too far from every block.

With the filled cells counted, a block can only stretch so far from them; cells beyond that reach are empty.

From one of our puzzles (15x15): In row 4 (clue 5 4), the filled cells already known pin the blocks: in the leftmost and the rightmost placement alike, G4 is empty.

Practise it: Nonogram puzzles at Hard

Full line analysistier 4

When: Check every arrangement of a line that fits the known cells; what they all agree on is certain.

When the simpler rules stall, list every arrangement of the line that fits the cells you know. Cells that are filled in all of them are filled; cells empty in all of them are empty. This catches joins and splits of blocks that the overlap rules miss.

From one of our puzzles (15x15): Every arrangement of column H (clue 3 1 1 3) that fits the known cells agrees: H7, H9 are empty.