The Overlap Method: the Only Trick You Really Need
If you learn one Nonogram technique, make it this one. When a block is longer than half its line, some squares are filled no matter where the block sits. And you can work out exactly which ones.
The idea in one sentence
In a line of length L with one block of size n: if 2n is bigger than L, then some squares in the middle are always filled. The count is 2n − L.
Why it works
A block of length n in a line of length L can start anywhere from square 1 to square L − n + 1. Push it all the way left: it covers squares 1 to n. Push it all the way right: it covers L − n + 1 to L.
The squares covered in both positions have to be filled, because every position in between covers them too. That overlap is 2n − L squares.
Example: 3 in a line of 5
A five-wide row with the clue 3. The block can start at square 1, 2, or 3.
- Start at 1: squares 1, 2, 3.
- Start at 2: squares 2, 3, 4.
- Start at 3: squares 3, 4, 5.
Square 3 is filled every time. Overlap = 2 × 3 − 5 = 1 square. So fill square 3 now, before you know where the block actually starts.
Example: 6 in a line of 10
A ten-wide row with the clue 6. The block can start at squares 1 through 5.
- Start 1: 1–6. Start 2: 2–7. Start 3: 3–8. Start 4: 4–9. Start 5: 5–10.
Squares 5 and 6 are covered every time. Overlap = 2 × 6 − 10 = 2 squares. Fill 5 and 6.
Columns work the same way
The method doesn't care if the line is a row or a column. Count the length, look at the block, apply the same arithmetic going downward.
In practice you alternate: run overlap on the crowded rows, fill what it forces, then check the columns those squares belong to. One forced square often creates another overlap in a column, and it cascades.
What if a clue has several blocks?
The simple version assumes one block. With several numbers, work out the line's minimum length first:
minimum length = sum of the blocks + one empty square for each gap
Compare that with the width. If the slack is small, the whole group has little room to move, and you can slide it left and right to find forced squares.
Example: a ten-wide row with 4 4. Minimum length is 9, so only one square of slack. Slide the whole arrangement between its two extreme fits and you'll find squares 2, 3, 4 and 7, 8, 9 are always filled.
Three mistakes to avoid
- Using it when 2n ≤ L. If the block is half the line or shorter, nothing is forced. A block of 2 in a line of 5 can sit in four places with no guaranteed square.
- Forgetting the gap rule with several blocks. Always add the minimum gaps first.
- Skipping the empties. The squares at the ends are often provably empty. Marking them matters as much as filling the middle.
Quick answers
What is the overlap method?
A way to find squares that must be filled. If a block of n sits in a line of L and 2n is greater than L, then 2n − L middle squares are always filled.
Does it need maths?
Just counting. You compare a block's size with its line's length.
Does it work with several blocks?
Not directly, because blocks shift independently. Add up the blocks and gaps first; if that total nearly fills the line, the same idea applies to the whole group.
What if the clue fills the whole line?
Then it's trivial: overlap equals the line length, so the whole line is filled.
Go practise it
Start small, where this one trick does most of the work. Play a free 5×5 Nonogram
Related: how to read Nonogram clues, the complete rules for beginners, and advanced Nonogram strategies. When 5×5 feels easy, move up to a 10×10 grid.