A confirmed filled fragment can sometimes force more cells of its clue block. Extending a confirmed block means using the clue length, the fragment's proven block identity, and surrounding boundaries to determine additional cells that the block must occupy.
The important word is must. A fragment should never be extended just because one direction looks plausible.
Example: an X boundary forces the rest of the block
Consider a 10-cell line with a single clue 5.
Cells 4–6 are filled, and cell 3 is confirmed empty:
??×■■■????
The five-cell block must include cells 4–6. Normally it could start in several positions, but the X at cell 3 prevents any placement that crosses that boundary.
The only legal placement is cells 4–8.
So cells 7–8 can be filled, completing the block.
The extension is forced because every other length-5 placement containing the known fragment would include the confirmed empty cell.
A grid edge can create the same effect
Suppose a clue 5 already has confirmed cells 1–3 filled at the left edge.
The block cannot extend outside the grid, so it must continue through cells 4–5.
This is the edge-specific version of the same general idea: a boundary removes alternative placements.
Confirm block identity before extending
On a multi-clue line, a filled fragment may still have ambiguous ownership.
For clues 3 5, a short run of two filled cells might eventually belong to either block depending on its location and the current X marks.
You cannot safely extend it to length 3 or length 5 until the clue assignment is proven.
Useful evidence for block identity includes:
- clue order and placement bounds;
- a separator that isolates the fragment;
- segment capacity;
- the impossibility of another clue reaching the fragment;
- a completed neighboring block that fixes the remaining order.
Extension is not the same as completion
Extension finds new filled cells that an unresolved block must include.
Completion means the block has reached its full clue length and can be closed with separators where appropriate.
A single deduction may do both. In the 5 example above, filling cells 7–8 extends the fragment and completes the block, after which cells outside the block can be marked empty because there are no other clues.
Use legal placements, not directional intuition
A reliable way to test an extension is:
- identify all legal placements of the clue block that include the known fragment;
- discard placements that cross X marks, violate separators, collide with other assigned blocks, or leave the line;
- intersect the remaining placements;
- fill only cells shared by all of them.
This shows that confirmed-block extension is closely related to constrained overlap. The known fragment and boundaries simply make the placement range much tighter.
When a fragment does not force extension
Take a 10-cell line with clue 5 and cells 4–6 filled, but no nearby X marks.
The block could occupy cells 2–6, 3–7, or 4–8, among other possibilities depending on all current constraints. The existing fragment by itself may not force either endpoint.
Do not choose a direction just to make progress.
If no additional cell is common to every legal placement, the correct action is to leave the endpoints unknown and inspect another line.
How to spot extension opportunities
Look for confirmed fragments that are:
- close to the grid edge;
- immediately beside an X mark;
- trapped inside a short open segment;
- associated with a large clue;
- uniquely assignable to one clue block;
- constrained by a completed neighboring block.
The more boundaries a fragment has, the fewer legal placements remain.
Common mistakes
Extending to the nearest boundary automatically
A block only needs to reach its clue length. It does not necessarily fill an entire segment.
Assuming adjacent filled fragments must join
Two fragments may belong to different clue blocks and require a separator between them. Joining and splitting is a separate deduction that must respect clue sizes.
Extending an unidentified fragment
If you do not know which clue owns the fragment, you may be using the wrong target length.
Filling every cell in the block's reach
Reach describes where a block may go. Extension fills cells the block must occupy. Keep union and intersection separate.
What to learn next
The natural companion technique is block reach. Instead of asking only which cells an identified block must fill, reach asks which cells it could possibly occupy — and therefore which cells lie outside every legal possibility.
FAQ
Can I extend a block from one filled cell?
Sometimes. If clue identity and boundaries constrain every legal placement enough to force additional cells, one anchor can be sufficient. Otherwise it is not.
Is block extension just overlap?
It uses the same intersection principle, but the important practical trigger is an already confirmed fragment combined with boundaries or other line constraints.
What should I do after the block reaches its clue length?
Treat it as completed, add any required separators, and use the resulting empty cells in the crossing lines.