Tuesday, 20 November 2012

Frogs' Legs & Bob Tails

Paris iPhone Photo Chronicles
~ Frogs' Legs & Bob Tails ~

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There's a classic logical teaser which can easily be applied to an agile rabbit, for example, and a frog on crutches, say.

They have a race. But seeing as how the agile rabbit is obviously far faster than the frog, especially now in his post-gastronomical state, there's a twist to the tale.

They are to race to a finish line a kilometre away. The croaker is graciously given a 100 metres head-start over the nibbler. The rabbit runs ten times faster than the unfortunate frog is able to hobble. And bang! they're off...

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The rabbit covers the 100m between them in a flash of fur, but by the time he does this, the frog's managed to cover 10m and is, therefore, 10m ahead of the rabbit.

The rabbit continues his onward rush, covering the remaining 10m quickly, but again the frog has covered a tenth of that distance, and is now precisely 1m ahead of the thundering furball.

Surely now the race will be well and truly over. The rabbit covers the last metre between the two competitors in the blink of an eye, by which time... the frog has covered an additional, painful... 10cm!

And so it goes on. The rabbit covers 10cm, the froggy 1cm. The rabbit 1cm; the frog is still one millimetre ahead. The rabbit a millimetre; the frog is a tenth of a millimetre ahead, etc. ad infinitum.

The rabbit can never overtake the frog, who will always be ahead, albeit by vanishingly small distances. N'est-ce pas?

And why not...
© 2012 
Sab Will / Paris Set Me Free - Contact me directly for photo tours, interviews, exhibitions, etc.

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