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Did you solve it? Do you think like an engineer?

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 Did you solve it? Do you think like an engineer?

Today I posed these two problems about curious objects. Here they are again with solutions.

1. Pythagoras Cup

Pythagoras, the Greek mathematician and mystic, is credited with having devised a cup with the following properties:

1) If you pour it up to a certain level it behaves like a normal cup.

2) If you pour it beyond that level all the liquid into the cup it is emptied through a hole in the bottom of the cup.

Can you draw the mechanism inside the cup?

The internal mechanism is very simple and has no moving parts. (If you are a plumber, this will be very easy for you.)

The cup is a nice metaphor for moderation in life. Fill it too much and you will lose everything.


Cross section of a Pythagorean cup being filled: in B, it is possible to drink all the liquid in the cup; but in C, the siphon effect causes the cup to drain Illustration: Nevit Dilmen

The cup has a central chamber that fills from the base of the cup, as shown above. The chamber is filled normally until the liquid overflows, creating a siphon that, thanks to gravity, will empty the batch. Toilets and the fabric softener tray in a washing machine use the same trick.

2. Upside down pot

Design a simple mechanism for a four-wheeled toy vehicle so that when you pull a piece of rope backwards out of the vehicle, the vehicle moves forward.


You will need to add a pulley system, like the one in the video above. The rope is wound around an axle which, when unwound, moves a belt that is connected to the axle of the wheel.

I hope you enjoyed today’s puzzles. I’ll be back in two weeks.

I’ve been putting together a puzzle here every other Monday since 2015. I’m always looking for great puzzles. If you would like to suggest any, please email me.

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