Earlier today I set you these two problems about curious objects. Here they are again with solutions.
1. Pythagoras’s Cup
![puzzle cup](https://i.guim.co.uk/img/media/784fd434f9f22f455ddc65dc961b9f8cfe159716/218_27_998_599/master/998.jpg?width=445&dpr=1&s=none)
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 hole 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](https://i.guim.co.uk/img/media/22a6bf04781343865fb3fe9c9aece73f37e305f6/0_0_19447_5749/master/19447.jpg?width=445&dpr=1&s=none)
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
![car puzzle](https://i.guim.co.uk/img/media/870e1eb081aad3cdaa004719a9c468cae12d7de5/257_0_1231_754/master/1231.jpg?width=445&dpr=1&s=none)
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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