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 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
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.
