Sum Search

Find the run of digits that adds up to each printed target — across, down or diagonally.

What it is

A word search whose vocabulary is arithmetic. The grid is digits 1–9; each target names exactly one straight run of four (by default) whose digits sum to it. The answer key rings them.

How to play

Work from the extremes. A target of 34 out of four digits needs 9+9+9+7 or better, so scan for clusters of nines; a low target needs a run of ones and twos. Middle targets are the hard ones — and this generator prints them only when they happen to be unique.

Why it is in the catalogue

The word lane’s arithmetic cousin, and a good demonstration that “unique answer” means different things in different puzzles. Here it is not about a solver: it is about whether the grid accidentally contains a second run reaching the same total.

The implementation’s guarantees

• Targets are read off the grid, not imposed on it. The first version chose runs, took their sums as targets, and rerolled filler digits until each target was hit once — a condition close to unsatisfiable, and the arithmetic says why: a 9×9 with four directions holds ~180 runs of four digits whose sums span only 4..36, about five runs per sum. No rerolling makes a mid-range sum rare, and each reroll perturbs dozens of runs at once; forty grids failed in a row. Tallying every run’s sum and printing only the sums that occur exactly once is cheaper and exact.
• A test re-verifies each target against every run in the grid, independently of the tally that produced it.
• Digits are 1–9, never 0: a zero lets two visibly different runs share a sum, which is the ambiguity the whole design is avoiding.
• Rating basis: run_length_and_directions — longer runs and diagonals are what make the scan harder, and the metadata says so.