The Overlap Technique in Nonograms Explained

If you learn only one nonogram method, make it the overlap technique. It is the single most useful tool in line solving, and it is the reason most easy and medium grids fall apart so quickly once you know it. The idea is simple: when a run of filled cells is long enough relative to its line, some cells are covered no matter where the run actually sits. Those cells are guaranteed, so you can fill them straight away. This guide explains exactly how overlapping in nonograms works, with the shortcut math and the multi-run version. New to the puzzle? Read how to solve nonograms first.

The core idea: slide left, slide right

Take any single clue on a line and do two thought experiments:

1. Push the run as far to the left (or top) as it will go.
2. Push the run as far to the right (or bottom) as it will go.

Any cell that is filled in both of those extreme positions must be filled in the real solution, because the run cannot avoid covering it. Cells that are only filled in one position stay undecided for now.

A worked example

Take a five-cell row with the clue 4.

• Slide the run left: it covers cells 1, 2, 3, 4.
• Slide the run right: it covers cells 2, 3, 4, 5.
• Cells 2, 3, and 4 are filled in both, so fill them.

You have just solved three of the five cells from a single clue, without looking at any other line. That is the power of overlap.

The shortcut: (2 × clue) − line length

You don't have to draw both positions every time. The number of guaranteed overlap cells in a line is:

(2 × clue) − line length

…whenever that result is positive. A few examples:

• Clue 4 on a 5-cell line: (2 × 4) − 5 = 3 cells.
• Clue 3 on a 5-cell line: (2 × 3) − 5 = 1 cell (the middle one).
• Clue 7 on a 10-cell line: (2 × 7) − 10 = 4 cells.
• Clue 6 on a 10-cell line: (2 × 6) − 10 = 2 cells.

If the number comes out zero or negative, that clue produces no overlap on its own yet. As a rule of thumb, overlap appears once a run is longer than half the line, and the longer the run, the more cells you get for free. That is why attacking the biggest clues first, a habit covered in our nonogram tips, pays off so well.

Overlap with multiple runs

Lines with several runs work the same way, you just pack all the runs together first.

Imagine a ten-cell row with the clue 4 3. Reserve one mandatory gap between the runs, so the runs plus the gap need 4 + 1 + 3 = 8 cells, leaving two cells of slack.

• Leftmost packing: the 4 covers cells 1–4, a gap at 5, the 3 covers cells 6–8.
• Rightmost packing: the 4 covers cells 3–6, a gap at 7, the 3 covers cells 8–10.
• Compare each run between the two packings. The 4 overlaps on cells 3 and 4; the 3 overlaps on cell 8.

So you can fill cells 3, 4, and 8 immediately. The trick with multi-run lines is to compute the leftmost and rightmost arrangement of the whole clue, then read off the overlap for each run separately.

Why overlap is the foundation

Overlap is special because it needs no information from crossing lines. Every other technique, edge logic, gap analysis, cross-referencing, builds on the cells overlap hands you for free. A typical solve looks like this: overlap seeds filled cells across the grid, those filled cells trigger edge deductions and gap analysis, and cross-referencing carries the chain into neighboring lines. Without the overlap opening, the rest has nothing to grip.

When overlap runs out

On hard and expert grids, fill percentages drop and runs get shorter, so overlap gives you less. That is by design. Once overlap stops producing cells, switch to gap analysis and cross-referencing, both covered in the techniques guide. But even on the densest puzzle, overlap is almost always the right first move, because it is the cheapest way to get the grid started.

Practice it

The fastest way to make overlap automatic is to drill it on small grids where the math is easy to see. Open an easy 5×5, find the biggest clue, and slide it left and right in your head. Once (2 × clue) − line length becomes second nature, you will fill the opening cells of any nonogram in seconds.