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Nonogram Edges: A Filled Square Near the End

The edges technique says: a filled square less than a block’s length from the start of a line must belong to the first block, so that block reaches at least a block’s length from the start. The same works from the other end with the last block. It’s how a single filled square near an edge turns into several.

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This is the third of the Nonogram techniques.

The rule

  1. Find the first square of the line that isn’t crossed out, and the first filled square.
  2. If the filled square is closer to the start than the length of the first block, the first block covers it.
  3. The block can’t start before the first open square, so it reaches at least to that square plus the block’s length: fill up to there.

Do the same from the other end with the last block.

Edges: a filled square near the start A row with the clue 4 and square 2 filled. The 4 must cover square 2 and can start no earlier than square 1, so it reaches at least to square 4: squares 3 and 4 are filled. 4 4 before after
The 4 must cover square 2 and can’t start before square 1, so it reaches square 4.

In a real puzzle

In the 10×10 every technique page follows, edges first come up at step 9. Column 6 needs a single 5, and rows 3, 5 and 7 are already filled. From the top, the filled square in row 3 is within 5 of the edge, so the 5 reaches at least row 5. From the bottom, the one in row 7 is within 5 of the bottom, so the 5 reaches back at least to row 6. Together, the 5 fills rows 3 to 7.

column 6, before and after column 6 with the clue 5, before and after this step. 5 5 before after
Column 6, drawn across: the 5 fills rows 3 to 7.
edges in the 10 by 10 puzzle The puzzle at step 9 of 49, just after this technique settles column 6 (clue 5). The squares it settled are highlighted. 2 1 3 2 6 2 1 2 2 3 1 2 4 9 5 3 2 3 3 6 6 1 4 1 6 3 5 5 2 2 1 2 1 2 3 1 2 3
The puzzle at step 9, with column 6 highlighted.

How often you’ll need it

On 100 of the game’s puzzles per size, edges were needed in 9 of the 5×5s, 52 of the 10×10s and 97 of the 15×15s. On big puzzles, with long lines and blocks that often start near an edge, it’s one of the most useful rules.

Next steps

Questions

Why does the filled square have to be the first block?

Because the first block can’t sit entirely before it: there isn’t room between the start of the line and the filled square. And blocks come in order, so if the first block covers it, it’s the first block.

Does it work from both ends?

Yes. A filled square close to the end of a line belongs to the last block, which then reaches back past it.