Neighbours (BrainBashers)

Neighbours is one of BrainBashers' Latin square puzzles. You fill a square grid so every row and column contains each number from 1 to the grid size exactly once. Between some pairs of adjacent squares there is a small bow-tie symbol: it means the two numbers are neighbours, differing by exactly 1, such as 3 and 4 or 2 and 1. The second rule matters just as much: where two squares touch and there is no symbol, their numbers must not be neighbours.

Kevin Stone's site posts a 4x4 Easy grid every day, then 5x5, 6x6 and 7x7 grids at Medium and Hard, and a 9x9 weekly special. A few numbers are given to start. Each puzzle has its own dated page with check, pencil marks, answer, print and restart, an option to show mistakes (a red dot marks two touching numbers that break a rule) and an optional clock, and a help page with a walkthrough.

The puzzles change at midnight GMT or at the time zone you set, and earlier days stay in the date list for four weeks; Random easy, medium and hard buttons serve extra grids beyond the daily ones. There are no adverts and no account.

It suits players who already enjoy Futoshiki or sudoku and want a variant where the empty borders carry as much information as the marked ones.

On a phone the 4x4 to 6x6 grids fit the screen, but the 7x7 and the 9x9 run past the right edge, so the larger sizes are easier on a desktop or tablet.