How to solve nonograms

Each number counts a run of filled cells in its row or column — the runs come in that order, with at least one empty cell between them.

Fill the cells you can be sure of, and cross out the ones you can rule out.

When every row and column matches its numbers, a small picture appears.

Two things follow from the rules and are worth saying out loud. Nothing ever needs a guess: every cell you fill or cross should be forced by the numbers, and if you find yourself gambling, there is a certain move you have not spotted yet. And rows and columns feed each other — a cell decided by a row is one more known cell in its column, which often unlocks that column in turn. Solving is this back and forth, not one line at a time.

Two kinds of line read at sight, before any counting: a 0 holds nothing — crossed end to end — and a 10 in a row of ten holds everything. Sweeping the board for these is the natural first pass; they are the easiest lines there are.

Between those extremes the same arithmetic still settles rows whole: add the clues to the gaps they must keep between them, and sometimes the sum is the whole line. Nothing is left to decide — the row simply draws itself out in order.

One clue, one line: when a run is longer than half its line, every possible position crosses the same middle cells. Those cells are certain before anything else is known — on most boards, the first marks come from here.

A filled cell against the border does more than sit there: the run that owns it is pinned to the edge, and drags the cells beside it along.

Filling cells is only half the game — crossing out the cells no run can reach is what keeps a board honest. Wherever a filled cell pins its run down, the far ends of the line open up.

A run that has reached its full length is finished, and a finished run has empty cells at both ends. Writing those crosses in — punctuating the runs — is how a half-done line starts answering questions.