A mole burrowed to make some underground rooms connected by tunnels so that each room had 3 tunnels from it, each tunnel leading to a different room. No two tunnels intersect (though one may pass under another). Among any 3 rooms, there are 2 of them which are not directly connected.
Prove that the mole can make 6 rooms with connections obeying these rules.
But we haven't even met!