June 23, 2024

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

1. Pythagoras’ Cup

Pythagoras, the Greek mathematician and mystic, is credited with designing a cup with the following characteristics:

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

2) If you throw it beyond that level all the liquid empty into the cup 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’re a plumber, you might find this very easy.)

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


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

2. Backward jalopy

Design a simple mechanism for a four-wheeled toy vehicle so that when you pull a piece of string 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 moves a belt connected to the wheel axle as it unwinds.

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

I’ve been doing a puzzle here on alternate Mondays since 2015. I’m always on the lookout for great puzzles. If you want to suggest one, email me.

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