The Impossible Puzzle

[Lee Oliver]

I came across this puzzle about 5 years ago and I have been working on it off and on ever since.  It's really quite the annoying little problem, does anyone want to take a crack at it?

This video introduces the rules and also why it is supposedly impossible.

<a href="http://www.youtube.com/v/hjAP8Fy5WhE&rel=1&fs=1&hd=1" target="_blank">http://www.youtube.com/v/hjAP8Fy5WhE&rel=1&fs=1&hd=1</a>

I think that I've got an idea but I need to confirm with some people first.

[Tglad]

I don't think there is a puzzle to crack here, it is just an impossibility, in fact I'd be surprised if it wasn't proved impossible quite a long time ago.

You could break some of the assumptions, like put it on the surface of a torus or something, but that is usually considered cheating

[David Makin]

There is no solution to the generic mathematical puzzle.

However if you take the case of the "real world" example then the solution is blatently obvious and also how gas, water and electricty should be supplied, you simply ensure that all 3 utilities are in the same location and thus all 3 can be routed to all properties the same way - this not only solves the puzzle but reduces the number of places where the road is likely to get dug up, probably saving councils an awful lot of money.