Mine Sphere

Minesweeper wrapped round a sphere. The globe is a Goldberg polyhedron: hexagons everywhere except twelve pentagons, which sit where the corners of an icosahedron would be. A hexagon has six neighbours, so its number counts up to six; a pentagon has five. The pentagons are tinted purple so you can spot them. There are no edges or corners: every cell is surrounded.

Five sizes, from 92 cells to 1,212, and three densities (15, 20 and 24 % mines). Six neighbours tell you more than eight do on a square board, so the densities are a little higher than the classic ones to keep them interesting.

Your first cell is never a mine, nor are its neighbours, so the first click always opens an area. Tick No-guess board and the mines are laid again and again until the solver can clear the board from your first cell by deduction alone. The solver uses only what you can see: single numbers, pairs of numbers where one’s hidden cells sit inside the other’s, an exhaustive check of small groups of cells along the edge of what you’ve opened, and the mines-left count. If no such layout turns up within a second and a half (it hardly ever takes more than a few tries), you get a normal board and the game says so at the end.