Two centipedes were walking along a country footpath when they met a ladybird.
“I’ve never met anyone with a hundred legs before,” said the Ladybird.
“I’m not sure I have either,” said the first centipede, called Centi.
“Nor me,” added the other, called Pede. “It’s actually a common misconception, ma’am.”
“So is that. I’m a male ladybird.”
“Sorry, sir. But some centipedes have only 30 legs,” said Centi.
“Some have 346,” said Pede.
“So how many have you guys got?” asked the Ladybird.
Centi and Pede looked at each other.
“Er—we prefer not to count them,” said Pede.
“In case we get confused and forget how to walk,” said Centi. “But our Mum did once tell us that if 12 of my legs were transferred to Pede, he’d have twice as many as me, and if 12 of his legs were transferred to me, I’d have three quarters as many as him. Maybe you can work it out from that.”
How many legs do Centi and Pede have?
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The answer Centi has 96 legs and Pede has 156. If Centi has c legs and Pede has p, then p+12 = 2(c-12) and c+12 = ¾(p-12). Therefore p = 2c-36 and 3p-4c = 84. So 3(2c-36)-4c = 84, that is, 2c = 192. This makes c = 96 and p = 156.
The winner was Dr Michael Blade, Aylesbury