The Doppit Almanac · No. 46

Runit

Fill each run with digits that follow on

What it is

Runit is a straights puzzle. The grid is black cells and white ones, and every straight line of white cells between the black ones is a run. Fill the white cells with digits, 1 up to the width of the grid, so no digit repeats in a row or column and every run holds digits that follow each other with no gaps.

The run rule is what makes it a puzzle rather than a Latin square. A run of three can hold 4, 5, 6 in any order but never 4, 5, 7, so one digit written into a run pins how far the rest of it can reach. Most white cells sit in a run across and a run down at once, and the digit they take has to suit both.

How it plays

• Fill every white cell with a digit from 1 up to the width of the grid.
• No digit is used twice in a row or twice in a column, counting straight through the black cells.
• Every run holds digits that follow each other, in any order: 3, 5, 4 is fine, 3, 5, 7 is not.
• A digit on a black cell counts for its row and its column, and belongs to no run.
• Tap a digit, then tap a cell to write it. Tap a filled cell to clear it.
• Notes writes small digits instead. Stuck? Hint names the next forced digit and says why.

The difficulties

Easy is five by five with about half the white cells already printed, a minute of reading a run's range off the one digit standing in it. Medium is seven by seven, roughly a third printed, where the runs and the lines have to be worked against each other. Hard is nine by nine with runs up to five cells long, and every board asks you at least twice to assume a digit, follow it a few moves, and find a run left with no digit it can take. Expert is a practice tier on hard's own nine by nine, with a third of the black cells taken away and hardly a digit printed. Supposing a digit is not enough there. You suppose one, work that board on until it needs a supposition of its own, and find the rules broken two levels down. It runs long, a quarter of an hour and more. A fresh board is dealt every day, for nothing.

Nearby in the almanac: Rankit, Digit and Skyit