Finders Keepers

Today's puzzle is a slight variant of one that has been used in Civil Service examinations.

The puzzle

Melchester Rovers are playing Fulchester United and by a strange quirk of fate there are three players in the Melchester team, a striker, defender and keeper respectively, that share the same name as one of the players in the other team. Fulchester's Wilkins lives in Fulchester; the Melchester striker lives midway between Fulchester and Melchester. Fulchester's Wilson gets £400 per match and Melchester's striker gets exactly one third as much as his next door neighbour, who is in the Fulchester team. The Melchester striker's namesake lives in Melchester. Melchester's Williams beats his team's defender at snooker. What is the name of Melchester keeper?

The solution

Fulchester's Wilkins lives in Fulchester, and either Fulchester's Williams or Wilson lives in Melchester. Melchester's striker lives midway between Fulchester and Melchester as a neighbour of one of the Fulchester team and he earns one third of that player's salary so that player can't be Fulchester's Wilson because £400 doesn't divide exactly by 3. So the Melchester striker's neighbour must be Williams. So Fulchester's Wilson lives in Melchester and is therefore the Melchester striker's namesake, i.e. the Melchester striker is Wilson. Now Melchester's Williams is not the defender and therefore Melchester's keeper is Williams.

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