### City Planning

**Source:**http://puzzles.nigelcoldwell.co.uk/twentysix.htm

**Problem:**

A man has built three houses. Nearby there are gas water and electric plants. The man wishes to connect all three houses to each of the gas, water and electricity supplies.

Unfortunately the pipes and cables must not cross each other. How would you connect connect each of the 3 houses to each of the gas, water and electricityic supplies?

**Disclaimer:**Trick Question!

**Solution:**http://puzzles.nigelcoldwell.co.uk/twentysix.htm

Seems like the pipes and wires do not all need to be in the same plane, in which case the problem is easy :)

ReplyDeleteIf we look at it from the point of view of Graph theory, it seems impossible, since K(3,3) is non-planar..

ReplyDeleteBut in this problem, you're allowed to modify the graph, so that there exists a "path" (not necessarily an edge) from every vertex on one side to every vertex on the other side. :)