TECHNIQUE 1 OF 4
Exact fit: account for the gaps
Before trying positions, work out how much room the clues require. Sometimes the runs and their separators use the whole line, leaving no decision about where anything goes.
The rule
Add the run lengths and one empty square between each consecutive pair. If that total equals the line length, place the runs in order with exactly those gaps. For example, clues 2, 2 require five squares: two filled, one empty, two filled. Clue 0 is the separate case in which every square is empty.
A common mistake
Adding only the filled squares overlooks mandatory separators. Clues 2, 2 cannot fit into four squares. Conversely, the rules do not require an empty square before the first run or after the last.
TRY IT 1 · nonograms-exact-fit-1
| C11 2 | C21 2 | C35 | C44 | C51 2 | |
|---|---|---|---|---|---|
| R12 | |||||
| R21 · 3 | |||||
| R33 | |||||
| R45 | |||||
| R51 · 3 |
What can you justify?
Use the exact fit technique. What does it prove about R2C1? Treat the displayed starting marks as established facts.
Written explanation
Row 2, clue 1, 3: 1 legal arrangement remains after respecting the current marks. Every arrangement agrees on R2C1 filled, R2C2 empty, R2C3 filled, R2C4 filled, R2C5 filled. Other undecided cells in this line are left open.
TRY IT 2 · nonograms-exact-fit-2
| C14 | C21 3 | C31 3 | C41 | C51 1 1 | |
|---|---|---|---|---|---|
| R12 · 1 | |||||
| R21 | |||||
| R33 · 1 | |||||
| R43 | |||||
| R55 |
What can you justify?
Use the exact fit technique. What does it prove about R3C1? Treat the displayed starting marks as established facts.
Written explanation
Row 3, clue 3, 1: 1 legal arrangement remains after respecting the current marks. Every arrangement agrees on R3C1 filled, R3C2 filled, R3C3 filled, R3C4 empty, R3C5 filled. Other undecided cells in this line are left open.
The shortest arrangement is not the only arrangement
Consider one seven-square line with clues 2, 2 and no marks. Number its positions 1–7.
The tempting move
Fill positions 1–2 and 4–5, then mark positions 3, 6 and 7 empty as the completed line.
Why it fails
That arrangement is legal, but not forced. Positions 3–4 and 6–7 can instead be the two runs. The minimum occupied span is five squares, leaving two spare squares that can change the placement.
What is actually justified
The exact-fit rule does not complete this line. Retain the legal alternatives and look for overlap or crossing information. A legal arrangement is not proof that it is the required arrangement.
Transfer the idea
A seven-square line has clues 1, 2, 2 and no marks. What is the complete line, and why can neither run move?
Check your reasoning
Fill position 1, leave 2 empty, fill 3–4, leave 5 empty, and fill 6–7. The runs use five squares and the two mandatory gaps use two. All seven squares are accounted for, so there is no spare space for a shift.