Tools & crafting Nonogram Puzzles

A hammer, a pickaxe, a scythe, a paint roller, a quill and an inkwell, a needle drawing thread, a mortar and pestle, a padlock hanging open. Most of what is on this shelf is an implement, and an implement is nearly always the same two things joined together: a handle and a head. That turns out to matter more for solving than the subject does.

A handle is a long straight stroke, and a long straight stroke is the single most useful thing a nonogram can hand you. The overlap rule — a run of length k in a line of n cells forces 2k − n cells wherever it sits — pays out in proportion to how long the run is, so a shaft that crosses two thirds of the board settles a column before you have made a decision of your own. The head is the opposite: a dense little cluster of short clues where every cell has to be argued out against the crossing line. Nearly every board here is that pairing, which means nearly every board has an obvious place to start and a definite place where the work is.

The craft subjects have a third shape worth naming: the pair. A needle with its thread, a mortar with its pestle, a quill resting in an inkwell — two masses with a deliberate gap between them. On a grid a gap is as informative as a block, and these boards are the best argument in the catalog for marking empty cells as carefully as filled ones. If you only mark what is filled, the space between the two objects stays ambiguous far longer than it needs to, and the crossing clues that would have resolved it go unused.

Difficulty here does not follow size, it follows whether the subject is solid or hollow. The boards rated hard are the implements drawn at an angle — a scythe blade, a pickaxe head, a pencil and an eraser seen in three-quarter view — because a diagonal on a square grid becomes a staircase of ones and twos, and the overlap rule gives a staircase nothing. The gentler boards are the ones standing upright and filled in: a bucket, an open padlock, an inkwell, a needle and thread. If you want a way in, take those first; a large upright object with a straight handle is the easier board even when it occupies more cells than a small tilted one.

Worth knowing before you pick: much of the shelf sits at fifteen cells a side, with the larger implements given a twenty-cell frame so the head has room to be recognisable. If you are moving up from ten-cell boards, the fifteen-cell tools are a reasonable next step precisely because of the handle — there is always something long to start on, which is not true of every category at this size.

There is a specific method for the head of a tool that is worth learning here and carrying elsewhere. Once the handle has fixed a row or a column, do not immediately start filling the cluster at the end of it; instead read the clues of the three or four lines that cross the handle at its top. The handle has already told you one cell in each of them, and a single known cell in a short crowded line is usually enough to pin its first run against the edge or against the cell you know. Work outwards from the join rather than inwards from the outline, and a hammer head that looked like a wall of twos and threes tends to fall in a handful of deductions.