Every arrangement is the slow, sure technique: list every way a line’s blocks can still fit, given what you already know, and settle any square that’s the same in all of them. It finds everything a single line can tell you. You only need it when the five quick techniques have nothing left anywhere on the grid.
This is the last of the Nonogram techniques.
The rule
- Pick a line with few unknown squares.
- Write out every way its blocks could sit: in order, one gap apart, never on a crossed-out square, covering every filled square.
- Fill any square filled in all of them, and cross out any square empty in all of them.
In a real puzzle
In the 10×10 every technique page follows, the quick techniques run out at step 41: none of them finds anything on any line. Row 1 needs a single 2. Squares 1 to 3 and 6 to 8 are crossed out, and square 5 is filled.
The quick rules don’t see what to do, because packing ignores filled squares: packed right, the 2 could sit in squares 9 and 10. But the 2 is the only block, so it must cover square 5. With square 6 crossed out, it can only be squares 4 and 5. There’s just one arrangement left.
That’s the only time this puzzle needs it. The remaining eight steps are quick ones.
A bigger example
The how-to-solve walkthrough has a line with three arrangements left, where the filled pair has to be the 2 of a 1 2 clue. Listing them shows three squares that are empty in all of them.
How often you’ll need it
On 100 of the game’s puzzles per size, every arrangement was needed in 7 of the 5×5s, 22 of the 10×10s and 70 of the 15×15s. On a big puzzle it’s a normal part of the solve: the average 15×15 needs it about six times.