Nonogram techniques beyond overlap — keep solving without guessing

When overlap is no longer enough

Overlap only looks at a clue’s two extreme seats. That is powerful when a clue is long relative to its line and weak when it is short: a clue of 3 on a ten-wide line has slack 7 and no overlap at all. Overlap also says nothing about empty cells, and it ignores the filled cells already sitting in the line.

The techniques below use exactly that missing information. They assume you can already fill, mark and work out the overlap on a single line — if not, start with how to play Nonograms and the overlap technique guide. Every example is a single ten-wide row; cells shown filled or × came from crossing columns.

Simple spaces: mark cells no block can reach

A cell that no legal placement of any block can cover is empty — mark it.

Overlap asks which cells every placement covers. Simple spaces ask the opposite: which cells does no placement cover? Here the row’s only clue is 2, and cell 5 is already filled. The block of two must include that cell, so it sits on cells 4–5 or 5–6.

The same test clears pockets that are too small. With a single clue of 3 and × marks on cells 3 and 8, the line splits into pockets of two, four and two cells. Only the middle pocket can hold a block of three.

On a line with several clues, ask the question block by block: a pocket is only safe to mark when it is too small for every clue that could still be placed there.

Edge forcing: filled cells near a border or wall

The 15×15 guide shows the simplest case: a filled cell on the very first square pins the first block. The rule reaches further. If a filled cell sits within the first K cells of a line, where K is the first clue, it can only belong to the first block — the second block cannot start that early. The first block must then cover every cell from that one through cell K.

Clues 4 2, with cell 2 filled. Cell 2 is within the first four cells, so it belongs to the 4. That block starts on cell 1 or cell 2, and either way it covers cells 2–4.

A × wall is an edge in the middle of a line. With a single clue of 3, cell 4 marked and cell 6 filled, the block cannot cross the wall, so it starts on cell 5 or 6.

Edge forcing works from both ends. Check the last clue against the end of the line as carefully as the first clue against its start.

Joining and splitting

Two filled cells with a short gap between them raise one question: are they part of the same block? If they must be, fill the gap (joining). If one block that long cannot exist, the gap is empty (splitting).

Joining: the only clue is 4, and cells 3 and 5 are filled. With one block in the line, both cells belong to it, so cell 4 between them is filled. A block of four that covers cells 3–5 sits on 2–5 or 3–6, so everything else is out of reach.

Splitting: clues 2 2, cells 4 and 6 filled. Filling cell 5 would create a run of three, longer than any clue in the line, so cell 5 must be empty.

Splitting is the more common of the two on real boards. Before filling any one-cell gap, compare the run it would create with the largest clue that could own it.

Clue ownership: which block does this cell belong to?

Once you know which clue a filled cell belongs to, every other technique gets sharper.

Ownership is usually proven in one of three ways: by size (a run of filled cells longer than a clue cannot belong to it), by position (a cell outside a block’s possible range cannot belong to it), or by order (blocks never swap places, so anything before a block belongs to earlier clues).

Clues 1 1 3, with cells 5 and 6 filled. A run of two cannot be either 1, so it belongs to the 3. That block sits on 4–6 or 5–7. If it started on cell 4, both 1s would need to fit in cells 1–2 with a gap between them — three cells of room in a two-cell space. So the 3 is on cells 5–7, and the two 1s take cells 1 and 3.

Ownership is also how you use the rest of this page on lines with several clues: assign the cell first, then apply simple spaces, edge forcing or overlap to that one block and its range.

Counting to finish lines

Two counts close lines quickly. First, the minimum length of a line’s clues is their sum plus one gap between each pair. If that equals the line length, the whole line is decided before you touch it.

Second, count the filled cells. When they add up to the clue total, every other cell in the line is empty — even if you have not worked out where each block sits.

The reverse count works too: if the open cells left in a pocket are exactly what its clue still needs, fill all of them.

The no-guessing approach

Never place a cell you have not proven. If a step feels like a guess, it is one.

Several techniques above ask “what if this cell were filled?” — splitting, the pocket test, the ownership example. That is not guessing. You check whether one line could still fit its clues, find that it could not, and mark the cell. A guess is different: it places a cell without proof and carries on, and every deduction after it inherits the risk. Nogramix puzzles are verified to have exactly one solution reachable by logic, so a stall always means a missed deduction, never a missing guess.

A pass that works when you are stuck

1. Re-run overlap on the longest clues, using every new × wall.
2. Mark simple spaces: cells and pockets no remaining block can reach.
3. Check filled cells near borders and walls for edge forcing.
4. Look at every short gap between filled cells: join it or split it.
5. Assign ownership wherever size, position or order proves it, then repeat steps 1–4 for that block.
6. Count: close lines whose fills reach the clue total, and fill pockets that are exactly full.
7. Move to the crossing lines of everything you changed.

Common mistakes

• Pinning a cell to the wrong block. Edge forcing only applies when the cell is within the first K cells, where K is the first clue. Further in, it might belong to a later block.
• Forgetting gaps when measuring reach. A block’s range shrinks by every neighbouring block plus its mandatory gap.
• Joining cells that could belong to different blocks. Joining needs proof that both cells share one block; with several clues, prove ownership first.
• Counting cells before they are proven. A count only closes a line when every counted cell is certain.

Practice in Spring Forest

In Spring Forest, the 10×10 chapters are a good place to start practising these techniques, and the 15×15 chapters reward them on almost every board. Browse the puzzle sizes and chapters, or read how to solve 15×15 Nonograms to see them combined on a full board. There is no timer against you, undo is free, and a hint reveals one proven cell when a line stalls.

Practice in Spring Forest

Start from the rules: how to play Nonograms. Review the first technique: the overlap technique. Go bigger: solving 15×15 Nonograms.