A bet? A game? Or nature?

Heh, I remembered something funny today. Some time in the early ’80s my father was the victim of a… bet. Greek men spend half of their lives in the cafeterias discussing usually things that they can not do anything about (e.g. politics). One day a guy showed up a puzzle and bet that no one can find a solution. My father bit.

The puzzle is this: you have 3 water fountains and 3 villages. You must connect all 3 fountains to all 3 villages but without their water lines ever get crossed. The water lines must be direct from each fountain to each village.

To save you a month of delirium and 500 sheets of paper, I will tell you right now that there is no solution to this puzzle. I don’t know why my father got sucked so much into this. Was that the sense of pride because of the bet? Was it simply the thrill of the puzzle itself? Or was that his human nature to solve problems?

My father has attended only few months of high-school (he ran off) but from all his 6 brothers and sisters he is the only one who is interested in “what’s out there” and trying to keep an open mind about stuff. It is him that I caught the bug from. I am more alike to my father than I am different (this also includes our bad temper and our donkey-like persistence).

3 Comments »

l3v1 wrote on March 12th, 2007 at 3:04 AM PST:

You know, there were some civilizations which found out that a water line doesn’t necessarily mean dig a half pipe in the ground and let it flow, but e.g. create a suspended (or on wooden legs) half-pipe waterline above the ground, or well, you also can build underground waterlines.

Yes, it’s not solvable in 2D in a plane, but well, the “puzzle” didn’t state you have to stay in a plane.


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Eugenia wrote on March 12th, 2007 at 6:02 AM PST:

The puzzle is 2D. It is meant to be solved in a piece of paper. But as I said, it does not have a solution as is.


KCorax wrote on March 17th, 2007 at 4:32 AM PST:

Ok here’s an easy to understand why this puzzle cannot be solved, and a way to find out if a graph can be drawn in a single stroke or not:

If a node in a graph is where you start from then it’s goind to have 1+2n lines attached to it. 1 because it’s where you started off and then 2 for each line that comes and goes. The same applies to the end node for the same reasons. Simple enough.

If a node is an intermediate one then its going to have 2n lines attached to it, beacause your pen will come and always go (1 + 1).

A special case is that the start node is also the end node so 1+2n +1+2k => 2(n+k)+2=> 2m . Therefore in such a graph all nodes have 2n lines attached to them.

Therefore (omitting some induction here) it holds that if in a graph there exist nodes with 2n+1 lines attached to them and their count is other than 2 or 0 the graph can’t be drawn in a single stroke.

This is basic topology theory, high school stuff really.


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