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Cloisters Summer Special 2006

Paul's Puzzle

Logonian Bouncing Beans

The moon of Logon Alpha is renowned throughout the civilised part of the Galaxy for its wonderful fairs. I remember the last time I paid a visit there, I came across a stall sporting a large jar of Logonian bouncing beans. The jar bore the label “Guess the number of beans and win the kitty”. Remembering that the stall holders were often rather keen on number games, I handed over 5 Logonian Kreeblies and guessed a number.

'4096,' I ventured.

'An interesting number, Sir,' came the reply, 'but too high.' I fished out another 5 kreeblies and guessed again. 'How about 3413?'

'Oh, another very interesting number, Sir. I take it that you are a bit of a mathematician. But still too high, I'm afraid.'

'I shall have a third and final guess, then. Let's try 1729.'

'Too small this time, Sir, although this too is an extraordinary number.'

'Do you know the properties of ALL the numbers from 0 to infinity?' I asked, amazed at his knowledge.

'Only half of them, Sir,' he replied with a wink and a smile. 'But it's getting late now, and it's the last day of the fair, so let me give you a clue. If I divide the number of beans by any number from 1 to 10 inclusive, the remainder is always 1 less than the divisor. And this is the smallest such number.'

I thought for a while, and then gave the answer.

'Correct, Sir, and here's the kitty.'

It was at that moment that I remembered that these stall holders also dabbled in word play, and I went away from the stall clutching a Logonian Mega-Pussy Cat.

How many Logonian bouncing beans were there?

This Puzzle has now closed!

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