Nonograms Strategies

Large blocks have fewer possible positions than small blocks. Look first for clues that:

Fill the entire line.
Almost fill the line.
Leave very little unused space.
Contain several large blocks.

A clue of 9 in a ten-cell line usually provides more information than a clue of 2.

Calculate the minimum space required by all the clues.

Use:

Minimum length = total of all clues + required spaces between the blocks

For a clue of 4 2 2:

4 + 2 + 2 + 2 required spaces = 10

If the line contains ten cells, there is only one possible arrangement:

■■■■×■■×■■

This is one of the easiest ways to begin a puzzle.

Place a block mentally as far left as possible and then as far right as possible. Any cells covered in both positions must be filled.

Consider a ten-cell line with the clue 8.

Leftmost position:

■ ■ ■ ■ ■ ■ ■ ■ · ·

Rightmost position:

· · ■ ■ ■ ■ ■ ■ ■ ■

The six central cells overlap:

· · ■ ■ ■ ■ ■ ■ · ·

Those six cells must be filled regardless of the final position of the block.

For one block, the number of guaranteed overlapping cells can be calculated as:

Guaranteed cells = 2 × block length − line length

For a block of 8 in a line of 10:

2 × 8 − 10 = 6

Therefore, six cells can be filled immediately.

Overlap also works when a line contains several clues, but each block must be compared only with itself.

Consider a ten-cell line with clues:

4 3

Earliest placement:

■ ■ ■ ■ × ■ ■ ■ · ·

Latest placement:

· · ■ ■ ■ ■ × ■ ■ ■

The first block of four overlaps in Cells 3 and 4.

The second block of three overlaps in Cell 8.

Therefore:

· · ■ ■ · · · ■ · ·

Be careful not to treat an overlap between two different clue blocks as a guaranteed filled cell.

When all clues in a row or column have been satisfied, mark every remaining cell in that line with an ×.

For example, a line with the clue 3 contains:

· ■ ■ ■ · · ·

Once the group of three has been identified, all other cells must be empty:

× ■ ■ ■ × × ×

In a black-and-white Nonogram, a completed block must have an empty cell immediately before and after it unless it touches the edge of the grid.

Clue:

3

Known block:

· · ■ ■ ■ · ·

After completing the block:

· × ■ ■ ■ × ·

These empty cells prevent the block from becoming longer than the clue allows.

A filled cell near the edge can force additional cells to be filled.

Consider a ten-cell line with the clue 5 and a known filled Cell 3:

· · ■ · · · · · · ·

The block of five must include Cell 3. It may begin in Cell 1, Cell 2 or Cell 3.

Possible placements:

■ ■ ■ ■ ■ · · · · ·
· ■ ■ ■ ■ ■ · · · ·
· · ■ ■ ■ ■ ■ · · ·

Cells 3, 4 and 5 are filled in every possible placement:

· · ■ ■ ■ · · · · ·

This technique is sometimes called edge forcing, wall pushing or gluing.

An × divides a line into separate available sections. Each section can be treated as a smaller line.

Suppose a line contains:

· · · × · · · · ·

If the first clue cannot fit in the area before the ×, it must be placed after it.

Known empty cells can therefore force blocks toward one side of the line.

If an available gap is smaller than every remaining clue, the entire gap must be empty.

For example, if the only remaining clue is 4, a gap containing only three unknown cells cannot contain that block:

× · · · ×

becomes:

× × × × ×

This is sometimes called the “does not fit” technique.

If a filled cell belongs to a particular clue, determine how far that block can extend.

For example, a line has the clue 4:

× · ■ ■ · · ×

The two filled cells cannot form a separate group because only one block of four is required. They must be extended until the group contains four cells.

Depending on the surrounding cells, some extension cells may become certain.

Two small groups of filled cells may have to be joined if they belong to one larger clue.

For example, with the clue 5:

■ ■ · ■ ■

The centre cell must be filled if these cells can only belong to the same block:

■ ■ ■ ■ ■

The opposite situation can also occur. If joining two groups would create a block longer than any available clue, the cell between them must be empty.

For example, if the largest remaining clue is 2:

■ ■ · ■

The unknown cell cannot be filled because that would create four consecutive filled cells:

■ ■ × ■

A cell must be marked empty if no remaining block can reach it.

This commonly happens:

• Near the edge of a line.
• Between completed blocks.
• Inside gaps that are too small.
• Beyond the maximum possible range of a clue.
• When a block has already been assigned to another part of the line.

This technique is sometimes called inaccessibility or range elimination.

Every new filled or empty cell affects two lines: one row and one column.

After making progress in a row:

1. Check the corresponding columns.
2. Add any new forced cells.
3. Return to the affected rows.
4. Continue alternating until no immediate deductions remain.

Do not remain focused on one part of the puzzle for too long. The next logical step may appear somewhere else in the grid.

When the exact position of a block is confirmed, mark or cross out its clue.

This helps distinguish completed blocks from unresolved ones and reduces mistakes in lines containing several clues.

Only fill a cell when it must be filled in every valid arrangement. Mark a cell empty only when it cannot be filled in any valid arrangement.

Blind guessing can create an error that does not become visible until much later. Well-designed Nonograms are intended to be solved through deduction.

Determine which clue a known group of filled cells can belong to.

For example, a line has clues:

2 5 2

If a group of four filled cells already appears near the centre, it cannot belong to either clue of 2. It must belong to the clue of 5.

Once the block has been assigned, its possible range becomes much smaller.