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Programming Enigma Puzzles

25 March 2016

Posted by on **From New Scientist #1486, 12th December 1985** [link]

“I’m not broke, but you’ve got more money than I have,” Bubbles complained.

“True,” said Hippocrene, blushing. “But less than twice what you’ve got. Now listen. If you square the money I’ve got, and add that to what you’ve got, you get the square of what Johnny’s got. See?”

“No,” said Bubbles, toying nervously with her beads. “I don’t see how you can square money.”

“That’s easy. Just express it as pounds. I mean the square of £1.20 is 1.44. The square of 15½p is 0.024025 — that is, 0.155². And so on. OK?”

“Yes,” said Bubbles, with a cheerful wink. “Go on.”

“And if you square yours and add that to mine, you get the square of Johnny’s too. Isn’t that amazing?”

“Moderately so.”

When this conversation took place, the halfpenny was still in use.

How much had Hippocrene and Bubbles respectively?

[enigma338]

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This Python program runs in 35ms.

Solution:Hippocrene had 62½p. Bubbles had 37½p.Johnny had 87½p.

Analytically:

Also:

So we only need to check

hin the range 50½p to 66½p (33 values).Here’s a Python program to save us the bother:

Line 16 can step in 200’s Jim

@Brian: You’re right, of course. That should speed things up a bit.