Problem from school days

[Eyefor]

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.


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[csl]

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[Eyefor]

Bugger.

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

For years I've been trying that!

Thanks (I think!).

 

[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.

 

[Eyefor]

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?

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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: