TECHNIQUE 2 OF 4
Overlap: keep only what every placement shares
A run does not need a known starting point to force some squares. Compare its possible positions and look for the section that survives every choice.
The rule
For a single run of five in a seven-square line, its possible starts are 1, 2 and 3. All placements fill positions 3–5, so those squares are certain. The others remain undecided. With several runs or existing marks, compare all arrangements consistent with those constraints; do not slide each run independently through other runs.
A common mistake
Filling the union of possible placements turns 'could be filled' into 'must be filled'. Only their intersection is forced. A long run also does not automatically settle both of its ends.
TRY IT 1 · nonograms-overlap-1
| C11 2 | C21 2 | C35 | C44 | C51 2 | |
|---|---|---|---|---|---|
| R12 | |||||
| R21 · 3 | |||||
| R33 | |||||
| R45 | |||||
| R51 · 3 |
What can you justify?
Use the overlap technique. What does it prove about R3C3? Treat the displayed starting marks as established facts.
Written explanation
Row 3, clue 3: 3 legal arrangements remain after respecting the current marks. Every arrangement agrees on R3C3 filled. Other undecided cells in this line are left open.
TRY IT 2 · nonograms-overlap-2
| C14 | C21 3 | C31 3 | C41 | C51 1 1 | |
|---|---|---|---|---|---|
| R12 · 1 | |||||
| R21 | |||||
| R33 · 1 | |||||
| R43 | |||||
| R55 |
What can you justify?
Use the overlap technique. What does it prove about R1C2? Treat the displayed starting marks as established facts.
Written explanation
Row 1, clue 2, 1: 3 legal arrangements remain after respecting the current marks. Every arrangement agrees on R1C2 filled. Other undecided cells in this line are left open.
Possible coverage is not forced coverage
A seven-square line has a single clue 4 and no marks. The run can start at position 1, 2, 3 or 4.
The tempting move
Fill all seven squares because every square is covered by at least one placement of the run.
Why it fails
The clue requires only four filled squares. Possible placements collectively cover the whole line, but only position 4 belongs to every placement.
What is actually justified
Fill position 4. Leave the other six squares unknown from this line alone. Certainty uses the intersection of possibilities, not their combined coverage.
Transfer the idea
An eight-square line has one clue, 5, and no marks. Which squares are forced filled? Is either end forced empty?
Check your reasoning
Positions 4 and 5 are filled in all four placements: 1–5, 2–6, 3–7 and 4–8. Neither end is forced empty because one placement fills position 1 and another fills position 8. All other positions remain unknown from this line alone.