The One Technique You Must Learn

If you only learn one nonogram strategy, make it the overlap method. It’s the foundation of every other technique, the first thing experts apply to any puzzle, and the reason most cells get filled in the early stages of solving.

The overlap method works by comparing the two extreme positions a block can occupy — pushed as far left (or up) as possible and as far right (or down) as possible. The cells that are filled in both positions must be filled in the final solution.

The Basic Formula

For a single block of size N in a line of length L:

Overlap = 2N − L

If the result is positive, that many cells in the center of the line are guaranteed filled. If it’s zero or negative, the overlap method alone can’t determine any cells for that clue.

Quick Examples

Block size (N)	Line length (L)	Overlap (2N − L)	Result
8	10	6	6 center cells are filled
6	10	2	2 center cells are filled
5	10	0	No overlap — nothing determined
3	10	−4	No overlap
10	10	10	Entire line is filled

Notice the pattern: the block must be more than half the line length for overlap to produce results.

Why It Works

Consider a block of 7 in a 10-cell line.

Leftmost position (block starts at cell 1):

■■■■■■■○○○

Rightmost position (block starts at cell 4):

○○○■■■■■■■

Overlap — cells filled in both:

○○○■■■■○○○

Cells 4 through 7 are filled regardless of where the block ends up. That’s 4 cells (2 × 7 − 10 = 4), matching the formula.

Multi-Block Overlap

With multiple blocks, apply the same logic but account for the other blocks and mandatory gaps.

Example: Clue “3 4” in 10 cells

Leftmost position — push everything left:

■■■○■■■■○○

Rightmost position — push everything right:

○○■■■○■■■■

Compare block by block:

Block of 3: leftmost cells 1–3, rightmost cells 3–5. Overlap: cell 3
Block of 4: leftmost cells 5–8, rightmost cells 7–10. Overlap: cells 7–8

Result: cells 3, 7, and 8 are confirmed filled.

Example: Clue “2 2 2” in 10 cells

Minimum space: 2 + 1 + 2 + 1 + 2 = 8. Slack: 2.

Leftmost: ■■○■■○■■○○ Rightmost: ○○■■○■■○■■

Overlap by block:

First 2: cells 1–2 vs 3–4 → no overlap (slack is 2, block is 2)
Second 2: cells 4–5 vs 6–7 → no overlap
Third 2: cells 7–8 vs 9–10 → no overlap

With 2 cells of slack and block size 2, no overlap occurs. This illustrates an important point: multiple small blocks often produce less overlap than one large block, even with the same total filled cells.

Overlap With Existing Information

The overlap method becomes more powerful when cells are already filled or marked X.

Constrained overlap

Suppose the clue is 5 in a 10-cell row, and cell 7 is already marked X:

The block of 5 can’t include cell 7, so it must fit within cells 1–6 or cells 8–10. It can’t fit in cells 8–10 (only 3 cells), so it must be in cells 1–6.

Now apply overlap within the reduced space: 2(5) − 6 = 4 cells of overlap. Cells 2–5 are confirmed filled.

This constrained overlap is where the technique truly shines. As you fill more cells and mark more Xs, the available space shrinks and overlap produces more results.

When Overlap Fails

The overlap method can’t help when:

The block is less than half the line length (no overlap)
Multiple small blocks spread across a large line (each block has too much room)
The line has no clues beyond 0

When overlap fails, you need other techniques: edge logic (blocks pinned to filled cells at boundaries), gap analysis (segments between X marks), and cross-referencing with perpendicular lines.

Practicing Overlap Speed

Experienced solvers calculate overlap mentally in under a second. To build this skill:

Memorize the formula: 2N − L. Practice on random number pairs until it’s instant
Spot high-overlap lines first: Scan the grid for the largest clues relative to line length
Process in priority order: High overlap lines first, skip lines with no overlap entirely

At noguelike.com, the roguelike progression starts with 5×5 grids where most clues have significant overlap. By the time you encounter 10×10 grids on deeper dungeon floors, calculating overlap should be automatic.

The Takeaway

The overlap method is elegant: one formula, universally applicable, produces guaranteed results. It won’t solve every cell, but it solves the first cells — and those first cells trigger cascading deductions that open up the rest of the puzzle. Learn it, internalize it, and every nonogram becomes approachable.