Common mistakes (and how to recover)

A nonogram is forgiving in that there's only one valid solution, so any mistake eventually surfaces. It's less forgiving in that the surfacing can be twenty cells later, when you've built more deductions on top of the wrong one and can't easily tell which deduction was the original.

Four mistakes tend to recur, and the recovery from each is different.

The off-by-one fill. You see a row with clue 5 on a line of length 10 and you fill in cells 4 through 8 because you did the overlap calculation wrong — or right, but for a clue of 7. The fix is to always work from the leftmost legal position to the rightmost legal position and mark the overlap, never to fill in "the middle of the run." If your finger goes for the middle, your eye is taking a shortcut your brain hasn't justified, and the off-by-one is waiting.

Cross-marks confused for fills. Most digital nonogram interfaces use distinct visual treatments for "filled," "cross," and "empty." Most paper nonograms use the same treatment — a small mark in the cell — for both filled and crossed-off, distinguished only by whether the mark is a square or an X. Under fatigue the X starts to look like a partial fill, and you treat the cell as part of a run. Cure: stop and look. If the row's runs no longer add up with the cells you think are filled, this is what happened.

Filling without reading the column. When the row gives you a deduction, the cells you fill participate in the column too, and the column has its own clue list. Filling a cell without checking that the column's clue list still works is the most common silent mistake — silent because the row is satisfied and the column won't disagree until you process its clue. If you've only been doing line-solving in one direction, switch directions periodically. Sweep the rows, then sweep the columns, then sweep the rows again with the new column information.

The phantom run. This is the meanest one. A clue of 2 1 3 reads, on tired eyes, as 2 13 — a run of two and a run of thirteen — which on a 10-line is impossible, and your eye reads the impossible clue as evidence of a different clue list entirely. By the time you've made several deductions on the wrong list, the puzzle is locked into an inconsistency that won't resolve. Cure: read clue lists out loud the first time, especially the longer ones, and especially the ones with adjacent single-digit numbers.

The recovery, in all four cases, is the same shape. When the puzzle stops resolving and you can't see why, the move isn't to look harder at the cells you've placed. The move is to walk every row and every column and check that the clue is satisfied by what's already filled. The first contradicted clue is at or near the cell where the mistake happened. Erase outward from there, in widening rings, until the puzzle resolves cleanly again. Half the time the wrong cell is one you placed five minutes ago and forgot you placed.

Mistakes don't cost the puzzle. Persisting in the wrong deduction does.