Nonogram Techniques: From Overlap to Edge Logic

Before you start

This guide picks up where How to Solve Nonograms leaves off. That one covers lines that add up exactly, the overlap, crossing out squares no block can reach, and finished lines. Here we look at lines that already have a few squares marked, which is where most of a medium or hard puzzle is solved.

In the diagrams, cream squares were filled before, grey crosses were crossed out before, and lime squares and orange crosses are the new deductions. Squares are counted from the left, starting at 1. Each picture was checked with the line solver that GameLake's own Teach me uses, so the lime and orange squares are exactly what the clue proves, no more and no less.

Glue: a filled square near a wall

A filled square so close to the edge of the grid that the first block and a gap couldn't fit in front of it must belong to the first block. That block can't start any further left than the edge, so it has to stretch at least its full length from there.

A cross works exactly like a wall. In the next row, squares 1 and 2 sit in front of a cross: too short for the 3, and the 2 can't come first, so they're empty. The filled square 5 must then be part of the 3, which starts at square 4 or 5 and always covers square 6. And because the 3 ends by square 7 at the latest, the 2 must start at square 8 or 9, so it always covers square 9.

Which block is this square?

With more than one block, the key question for every filled square is which clue number it belongs to. Try each block in turn and throw out the ones that leave no room for the others. Once you know the owner, glue and overlap do the rest.

Working from the far end like this is easy to forget. Clues are read left to right, but the last block is just as stuck against the right-hand wall as the first block is against the left.

Mercury: the block pulls away from the wall

Sometimes a filled square proves that the edge square is empty. If a filled square sits exactly as far from the wall as the first block is long, that block can't fit in front of it, so it has to run through it, and then it can't reach back to square 1. The name comes from the way mercury pulls back from the sides of its glass.

A run of filled squares pushes even harder. Two filled squares at 3 and 4 in the same row would also rule out square 1, because the 3 must cover both.

Joining: two squares, one block

When two filled squares must belong to the same block, every square between them is filled too. The simplest case is a line with a single clue, but it works whenever the squares in between can't hide the end of one block and the start of the next.

Splitting: two squares, two blocks

The opposite check: if joining two filled groups would make a block longer than any clue, the square between them must be empty. That split usually tells you which block is which, and the rest follows.

Simple contradictions: what if?

When nothing above applies, test one possibility. Suppose a square is filled (or that a filled square belongs to a particular block) and follow the line through. If that leads to something impossible, a block with no room or a filled square no block can cover, the opposite must be true.

Inside one line, this is safe and quick. Puzzle books also use contradictions across the whole grid: fill a square, follow the consequences through the rows and columns it crosses, and see if something breaks. It works, but it's slow and easy to get wrong without a pencil, and a good puzzle rarely needs it. No GameLake nonogram ever does: every puzzle is checked by a solver that only uses one line at a time, so there is always a single-line deduction somewhere on the board.

A routine for harder puzzles

1. Fill the overlaps on the biggest clues, rows first, then columns.
2. Every time you fill or cross a square, look at the other line through it. That's where the new information goes.
3. For each line with marked squares, ask which block each filled square belongs to. Then glue it to the nearest wall or cross.
4. Check pairs of filled squares: join them if they must be one block, split them if they can't be.
5. Cross out finished blocks on both sides, and lines whose clues are all drawn.
6. Still stuck? Pick the line with the fewest open squares and try a what-if.

Tap Teach me on GameLake whenever you want a nudge. Hop names the line, highlights the squares and explains the step, using the same ideas as this page: a block that always covers some squares, a block that can only go in one place, squares no block can reach, a complete block that needs a cross beside it, or, for the trickier cases, that the squares are filled (or empty) in every way the clue can fit.

Frequently asked questions

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