The Doppit Almanac · No. 37

Chainit

Fill every cell so the numbers run in order

What it is

Chainit is a number chain. The grid holds every number from 1 up to the number of cells, one to a cell, and numbers one apart sit in cells that touch, including corner to corner. Some of the numbers are printed. The rest are yours to work out.

A corner counts as touching, so a cell in the middle of the board has eight ways on rather than four, and where the next number goes is a real question. Two things do the work. You follow the chain a number at a time, wherever a printed number has only one free cell beside it. And you count: the 17 and the 21 are four numbers apart, so the cells holding them cannot be more than four steps apart either, which rules out most of the board at a stroke.

How it plays

• Fill every cell with a number, from 1 up to the number of cells.
• Every number is used once, and every cell holds one.
• Numbers one apart sit in cells that touch, including corner to corner.
• The 1 and the last number are always printed for you, and printed numbers cannot be changed.
• Tap a digit, then tap a cell to write it. A number past 9 takes both its digits on the same cell: 1 then 2 writes 12.
• Erase empties a cell. A number that clashes glows red, and Hint names the next number that is forced.

The difficulties

Easy is five by five, so the numbers run to 25 and more than half of them are printed: half a minute of following the chain. Medium is seven by seven, where counting the steps between two printed numbers starts carrying whole stretches on its own. Hard is nine by nine with half the numbers rubbed out, and most boards need two or three places where you put a number in a cell, follow it a move or two, watch the board run out of room, and take it back out. Expert is the same nine by nine with only a third of the numbers printed. You do that a dozen times a board, and in between you ask where a number's neighbours could go, because often only one cell leaves them both room. A fresh board is dealt every day, for nothing.

Nearby in the almanac: Trackit, Summit and Digit