**From New Scientist #1429, 8th November 1984** [link]

Apart from providing the beer at my birthday party, I decided to encourage the abstemious by paying every guest a bounty of 10p for every pint drunk by someone else *minus* 20p for every pint he drank himself. I can’t remember all the details, but I do know that I paid out £9 in bounty altogether. Each guest drank a different odd number of pints, and everyone received some bounty money except David, who consumed so much beer (no one else’s consumption was within 3 pints of his) that he got exactly nothing in bounty.

From that information you can probably work out just how much each guest drank. If you do, please let me know.

[enigma282]

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Using units of 10p, if we have

npeople who drinkp_1, p_2, …, p_npints (lets say in descending order).Then, if

tis the total number of pints drunk:And the bounty for the

k-th person is:David, the person who drinks the most, gets zero bounty, so:

Also the total of all the bounties is 90 units:

So we can consider the divisors of 90.

This Python3 program runs in 54ms.

Solution:The guests drank (in decreasing numbers of pints): 15 pints (David), 11 pints, 9 pints, 7 pints, 3 pints.So, a total of 45 pints were consumed by the 5 guests. (Quite a boozy party).

The corresponding bounties are: 0p (for David), £1.20, £1.80, £2.40, £3.60.

I’m not quite sure why the setter wrote “from that information you can

probablywork out just how much each guest drank” – maybe he had had a couple of pints too many himself.