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Gap Elimination

Learn how to mark an open Nonogram region empty when it is too short to contain any clue block that could still belong there.

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Gap elimination marks cells empty when an open region is too short to hold any clue block that could legally occupy it.

The idea is simple: if no remaining block can fit inside a region, none of its cells can belong to the solution.

Concept diagram

Example: a three-cell region cannot contain a block of four

Take a 10-cell line with a single clue 4. Suppose cell 4 is already confirmed empty:

??? × ??????

The empty mark creates two open regions. The first is only three cells long. A block of four cannot fit there, so cells 1–3 are all forced empty.

Line example
Clues4
Given
Result

The block must therefore be somewhere in the six-cell region to the right.

This does not yet tell you its exact position. Gap elimination removes impossible space; another technique such as overlap may then find forced filled cells inside the surviving region.

Techniques · BeginnerThe Nonogram Overlap MethodLearn the Nonogram overlap technique using earliest and latest block placements, see why the shared cells are forced, and apply overlap to constrained segments.

What counts as an open region?

Confirmed empty cells divide a row or column into contiguous areas that may still contain unresolved blocks. VeyraPlay calls these areas open segments.

For gap elimination, ask two questions:

  1. which unresolved clue blocks could legally belong to this segment?
  2. is the segment long enough for at least one of them?

If the answer to the second question is no for every compatible block, the whole segment is empty.

Techniques · IntermediateLine SegmentationLearn how X marks divide a Nonogram line into open segments, how segmentation reduces placement freedom, and when separate regions can be solved as smaller clue problems.

Compare against compatible clues, not just the smallest number

A common shortcut is to compare a gap with the smallest remaining clue. That is safe only if every remaining clue is genuinely able to occupy that region.

Clue order, completed blocks, separators, and already assigned segments may rule some clues out. A two-cell segment might be large enough for a clue 2, for example, but still be empty if that 2 is already known to belong elsewhere.

So the precise rule is:

eliminate a segment when no legal remaining clue assignment can place a block inside it.

This becomes increasingly important on multi-clue lines.

Techniques · IntermediateAssigning Clues to SegmentsLearn how to assign Nonogram clue blocks to open segments using clue order, capacity, completed blocks, and known filled cells without making unsupported guesses.

Gap elimination after completing a block

Completed blocks often create the best opportunities.

Once a clue block is finished and separated correctly, the remaining clues have less space available. A small leftover region that looked plausible earlier may suddenly become too short for every unresolved clue.

That region can then be crossed out completely.

This creates a useful sequence:

  1. finish a block;
  2. place its mandatory separator;
  3. recalculate the remaining open segments;
  4. eliminate segments that cannot contain any unresolved block;
  5. re-scan the line.
Techniques · BeginnerCompleted Blocks and SeparatorsLearn how to recognize completed Nonogram blocks, place mandatory empty separators beside them, avoid accidental merging, and use finished clues to simplify lines.

Gap elimination and block reach are two views of the same constraint

G-030 asks which cells a block can still reach. Gap elimination asks whether an entire region is outside the reach of every relevant block.

If no block can reach any cell in a segment, the segment is forced empty.

The segment-based view is usually easier for a human player because confirmed X marks make the boundaries visible immediately.

Techniques · IntermediateBlock Reach and Unreachable CellsLearn Nonogram block reach, find the union of legal block placements, identify cells no clue can occupy, and turn impossible positions into confirmed empty cells.

Step-by-step method

When you see several X marks in a line:

  1. identify the open segments between them;
  2. note which clue blocks remain unresolved;
  3. use clue order and known block assignments to identify which clues could occupy each segment;
  4. compare each segment length with those clue sizes;
  5. if none can fit, mark the entire segment empty;
  6. check whether the new X marks create stronger deductions elsewhere.

Common mistakes

Eliminating a region because the largest clue does not fit

A smaller unresolved clue may still fit. You need to exclude all compatible clues, not just one.

Ignoring clue order

A segment may physically fit a block but lie on the wrong side of blocks that must appear before or after it.

Treating an unknown cell as a separator

Only confirmed empty cells divide the line. Unknown cells remain available to blocks.

Filling the surviving region automatically

Eliminating one region tells you where a block cannot go. It does not necessarily tell you exactly where it must go inside the remaining space.

What to learn next

Gap elimination naturally leads to line segmentation. Once several empty separators are confirmed, it becomes useful to stop thinking about the row or column as one long line and solve its open segments as smaller constrained problems.

Techniques · IntermediateBlock Reach and Unreachable CellsLearn Nonogram block reach, find the union of legal block placements, identify cells no clue can occupy, and turn impossible positions into confirmed empty cells.Techniques · IntermediateLine SegmentationLearn how X marks divide a Nonogram line into open segments, how segmentation reduces placement freedom, and when separate regions can be solved as smaller clue problems.Techniques · IntermediateAssigning Clues to SegmentsLearn how to assign Nonogram clue blocks to open segments using clue order, capacity, completed blocks, and known filled cells without making unsupported guesses.

FAQ

Is gap elimination only for tiny gaps?

No. Any open region can be eliminated if no unresolved clue block can legally occupy it.

Can a segment be too small for one clue but usable by another?

Yes. That is why you must consider clue compatibility and order before crossing out the whole region.

Is this the same as marking cells outside block reach?

They are closely related. Block reach works cell by cell or block by block; gap elimination is the segment-level consequence when an entire region is unreachable.