Solution: A game of avoiding the neighbours
Solution to puzzle for 22 April 2008.
The insight needed for speedy solving is to realise that each central number links directly with six others, and thus cannot be other than 1 or 8. For example, if 3 were to be centrally placed, it would be barred from linking with both 2 and 4, despite already linking by definition with six others. This would require the diagram to have nine numbers rather than eight.
Back to puzzle: a game of avoiding the neighbours.