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Nonogram Overlap: Fill What Every Position Shares

The overlap is the squares a block covers both when the line’s blocks are packed as far left as they go and when they’re packed as far right. Wherever the block really sits, it covers those squares, so they’re filled. It’s the first technique to learn, the one that starts every puzzle, and the one you’ll use most.

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This is the second of the Nonogram techniques.

The rule

  1. Pack the line’s blocks as far left as they go: in order, with one gap between each, and never on a crossed-out square.
  2. Pack them as far right as they go.
  3. Fill every square that a block covers both times.
The blocks 3 and 4 packed left, then right The same row twice. On top, the 3 sits in squares 1 to 3 and the 4 in squares 5 to 8. Below, the 3 sits in squares 3 to 5 and the 4 in squares 7 to 10. Square 3 is covered by the 3 both times, and squares 7 and 8 by the 4. 3 4 3 4 packed left packed right
3 4 packed left, then right.
Overlap: 3 4 in ten squares An empty row with the clue 3 4. Packed left and packed right, the 3 covers square 3 both times and the 4 covers squares 7 and 8, so those three are filled. 3 4 3 4 before after
So the 3 always covers square 3, and the 4 squares 7 and 8.

On an empty line there’s a shortcut: the slack is the line’s length minus what the clue needs (the runs plus one gap between each). A block longer than the slack has length minus slack certain squares. See the rules page, where we check this on every clue for lines of 5 to 10.

In a real puzzle

The 10×10 every technique page follows opens with an overlap. Row 3 needs 2 6, which takes 2 + 1 + 6 = 9 of its 10 squares: the slack is 1. The 2 gets one certain square and the 6 gets five.

row 3, before and after row 3 with the clue 2 6, before and after this step. 2 6 2 6 before after
Row 3, 2 6 with a slack of 1: square 2 and squares 5 to 9 are filled.
overlap in the 10 by 10 puzzle The puzzle at step 1 of 49, just after this technique settles row 3 (clue 2 6). The squares it settled are highlighted. 2 1 3 2 6 2 1 2 2 3 1 2 4 9 5 3 2 3 3 6 6 1 4 1 6 3 5 5 2 2 1 2 1 2 3 1 2 3
The puzzle after its first step.

The puzzle uses the overlap 26 times in its 49 steps, more than any other technique.

How much it does

On 100 of the game’s puzzles per size, the overlap was used on average 7.7 times per 5×5, 21.8 per 10×10 and 41.8 per 15×15. The overlaps on the empty grid alone give 80% of a 5×5’s picture, 63% of a 10×10’s and 49% of a 15×15’s. See tip 1.

Next steps

Questions

What's the slack?

The line’s length minus what the clue needs: the runs plus one gap between each. A block longer than the slack has that many fewer certain squares than its length.

Does the overlap only work on an empty grid?

No. Crossed-out squares push blocks inwards when you pack them, so a line can overlap later in the puzzle even if it didn’t at the start.