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

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

Earlier today I set you these two problems about curious objects. Here they are again with solutions.

1. Pythagoras’s Cup

Pythagoras, the Greek mathematician and mystic, is credited with devising 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 of the liquid in the cup empties through a ***** at the bottom of the cup.

Can you draw the mechanism inside the cup?

The mechanism inside is very simple and has no moving parts. (If you are a plumber you might find this very easy.)

The cup is a cute metaphor for moderation in life. Fill it up just a little too much and you will lose everything.

Solution

Cross section of a Pythagorean cup being filled: at B, it is possible to drink all the liquid in the cup; but at 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 above. The chamber fills up as normal until the liquid spills over, creating a siphon which thanks to gravity will empty the lot. Flush toilets and the fabric softener tray in a washing machine use the same trick.

2. Backwards jalopy

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

Solution

You’ll need to add a pulley system, like the one in the video above. The string is spooled around a shaft, which when it unwinds moves a belt that is connected to the wheel axle.

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

I’ve been setting a puzzle here on alternate Mondays since 2015. I’m always on the look-out for great puzzles. If you would like to suggest one, email me.

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