In this game there is a grid of 22 triangles, four of which are painted. You may initially place a tetrahedron on any triangle you want but from there forward you move by ‘rolling’ the tetrahedron over one of its edges so that it will then be on an adjacent triangle on the grid and resting on a different face of the tetrahedron. If you roll onto a painted triangle, the paint transfers to that face of the tetrahedron (unless that face is already painted), and when a painted face of the tetrahedron lands on an unpainted triangle, the paint is transferred from the tetrahedron to the triangular grid.

The object of the game is to continue to roll around the grid until all four faces of the tetrahedron are painted, however only one of the four grids shown can actually be solved. The other three are not solvable regardless of where the tetrahedron is initially placed.

Which is one that can be solved?