# Thread: Problem from school days

1. ## Problem from school days

Right.

I'm on a roll now.

After 30+ years of searching I've finally located the riverside meadow where, in the 50's, my parents took us kids to swim in the river so I would like assistance please with this little problem that I have failed to solve since my school days despite countless attempts.

Some little ****e at school told me the below shape can be drawn without removing the pen / pencil from the paper.

I've started in the middle, done the outside semi-circles first, etc etc and still haven't solved it.

Maybe it can't be done (in which case I will next search out that little ****e and give him a well deserved smack in the gob) or maybe someone can crack it for me?

Thanks.

2. Bugger.

That is cheating. I'm gonna smack him in the gob now anyway.

For years I've been trying that!

Thanks (I think!). ;-)

3. There is another one you should try.

Draw three houses in a line, to save time I just draw 3 boxes. Then below each house draw a factory, again just a simple box will do. Each factory represents a utility (Gas, Water and Oil). Each house needs to be supplied with all three utilities but the pipes can not cross over each other. Have a go.

4. Originally Posted by rogue trader
There is another one you should try.

Draw three houses in a line, to save time I just draw 3 boxes. Then below each house draw a factory, again just a simple box will do. Each factory represents a utility (Gas, Water and Oil). Each house needs to be supplied with all three utilities but the pipes can not cross over each other. Have a go.
There are three houses and three utilities:
You must draw a line from each house to each utility, without the lines ever crossing. Can you connect the houses to the utilities?

This problem is impossible. At least, it's impossible to connect the houses to the utilities on a flat sheet of paper. In fact, it's impossible in the Euclidean plane (a flat sheet stretched to infinity) and on most other two-dimensional surfaces. Some people have a trick to get around the problem: they send a gas, water, or electric line through one of the houses. Of course, real utility companies don't need tricks. The real world is three-dimensional, so power lines can go over or under each other.
The three utilities puzzle can be solved on a special kind of two-dimensional surface. This special place is the outside of a torus. A torus is shaped like a perfect doughnut, with a hole in the middle. You can see a movie of a flat surface becoming a torus at Alexander Bogomolny's page about Paper Strip Activities. Here's one solution:

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