What is the overlap method in Nonograms?

If a block of size n sits in a line of length L and 2n is greater than L, then 2n minus L cells are forced to be filled, in the middle of the line. Filling those guaranteed cells is often the fastest way to start a puzzle.

Should I guess when solving a Nonogram?

No. A well-made Nonogram has a unique logical solution, so if you feel the need to guess, re-read the rows and columns you have already worked on to find the deduction you missed.

What order should I solve a Nonogram in?

Start with the longest clues and any clue that fills an entire line. Then alternate between rows and columns, marking empties with X as soon as you prove them.

How to Solve Nonograms

This tutorial teaches the two techniques that solve the large majority of a typical Nonogram. Work through it once and you will be able to finish most 5×5 and 10×10 puzzles without guessing.

Step 1: Understand the clues

Each number next to a row or column is the length of a block of filled cells. Clue 2 3 means: a block of two, at least one empty cell, then a block of three. The order never changes.

Step 2: Start with clues that fill the whole line

If a clue equals the length of the line, the whole line is filled, so no deduction is needed. In a 5-wide row, a clue of 5 fills every cell.

Step 3: Use the overlap method

This is the single most useful Nonogram technique. Take a line of length L containing one block of size n. If the block is longer than half the line (2n > L), then some cells are filled no matter where the block sits.

The overlap is 2n − L cells long, and it always sits in the middle of the line. For example:

Line length 5, block of 3 → overlap 2 × 3 − 5 = 1 cell. With a block of 3 in a 5-wide line, the third cell is always filled.
Line length 10, block of 6 → overlap 2 × 6 − 10 = 2 cells. The block must cover cells 5 and 6.

Fill those guaranteed cells first. They often unlock the next row or column.

Step 4: Mark the empties with X

Every cell you prove empty is just as valuable as a filled cell. Marking empties stops you from re-checking the same options and reveals where blocks can start. Once a cell is proven empty, mark it and move on.

Step 5: Work the intersections

After filling or marking a row, immediately check the columns that cross it. A new filled cell may complete a column clue, or an X may rule out a position for a column block. Solving is a loop: row, column, row, column.

Step 6: Count from the edges

Look at where a block can sit if it starts at the far left and ends at the far right. Comparing those two extreme positions shows which cells are always covered. This is a variation of the overlap method that also works with multiple blocks in a line.

Step 7: Never guess

If you find yourself guessing, stop and re-check the clues you have already used. On a puzzle with a unique solution, there is always another deduction available. Guessing leads to a board full of contradictions and is much slower than re-reading a row carefully.

Practise

Try a 5×5 puzzle and apply steps 2 to 4. When you can finish those comfortably, move up to 10×10, then 15×15. If you get stuck, the Hint button applies exactly one logic deduction for you, and studying what it does is a fast way to learn.