The second technique
Edge logic
The ends of a line are where a run has the least room to move. That is what makes an edge square worth reading first: settling one there usually settles several more.
The first square belongs to the first clue
A run cannot start before the line does, so a filled square in the first position can only be the beginning of the first clue. The whole run drops into place from there, and the square immediately after it must be empty — otherwise the run would be longer than its clue says.
Take a 15-wide line with clues 5 4. Its slack is 5, so neither clue is longer than the slack and overlap finds nothing at all. Fill in square 1 from a crossing line and the picture changes completely: the 5 has to occupy squares 1 to 5, and square 6 has to be empty. One square bought five.
A cross at the edge is worth as much as a fill
Crossing out a square at the end of a line shortens the line the runs actually have to live in, and a shorter line means less slack for every clue in it. This is the deduction players skip most often, because a cross feels like the absence of information rather than information.
A 10-wide line with a single clue of 7 has slack 3 and overlaps four squares. Cross out square 1 and the clue now lives in nine squares instead of ten, so the slack falls to 2 and the overlap grows to five squares. The cross paid exactly as much as filling a square would have.
Both ends, every pass
Edge logic applies at the last square exactly as it does at the first — a filled square in the final position belongs to the last clue, and the square before the run is empty. Reading a line right to left is not a different technique, and lines whose right end you never check are the usual reason a sweep stalls halfway.
When the edge is not settled yet
If neither end of a line carries a mark, edge logic has nothing to work with, and the line is waiting on a crossing square rather than on you. That is the normal state early in a grid. It is also why the opening sweep is overlap's job: overlap is the only technique that pays on a line where nothing at all is known.
Common questions
- What is edge logic in a nonogram?
- It is what you can deduce from a square at either end of a line. A filled square in the first position can only belong to the first clue, and that clue has nowhere to start except right there — so the whole run drops into place, and the square after it is empty.
- Why does a filled square at the edge do more than one in the middle?
- Because a run reaching a middle square can be positioned either side of it, while a run reaching the first square has only one way to sit. The edge removes the ambiguity that makes middle squares slow to resolve.
- Is a cross at the edge worth anything?
- Yes, and often as much as a fill. A crossed-out square at the end shortens the usable line by one, which lowers the slack for every clue in it. On a 10-wide line with a single clue of 7, one cross at square 1 turns a four-square overlap into a five-square one.
- Should I check edges before or after overlap?
- Overlap first on an empty grid, because it needs nothing to be known. After that, check the edges of every line that has picked up a mark — edge logic is the technique most likely to pay on a line overlap has already been over.