Tuesday, 22 April 2025

Maths: Two quickies

 The mystery diagonal

What is the value of AC?

You have 30 seconds: what is the length of the blue diagonal, AC? This is one of those questions where the time limit tells you there must be an easy answer.

Give up? Think about a line that isn't drawn, even though it is mentioned in the title...

Full of germs

A bacterium divides in two, every 20 minutes. At exactly noon on January 29, one bacterium is dropped into a culture vessel, and at exactly noon on January 30, the vessel is found to be completely full. At what time was the vessel half full? As you will see when you work out the answer (or peek at the note below), you need an agile mind. There has to be an answer…

And this time, you get help: Anybody who knows (and worries) about human populations knows the answer to this. If the population doubles every 20 minutes, the vessel was half full at 11:40 pm on January 30.

See? It’s all a matter of thinking outside the box, both you and Schrödinger’s other cat. (Yes, that's another in-joke.)

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