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Programming Enigma Puzzles

20 December 2017

Posted by on **From New Scientist #1016, 2nd September 1976** [link]

Paul Pennyfeather, you will recall from Evelyn Waugh’s novel, was sent down from Oxford and went to teach in Dr Fagan’s horrid school at Llanaba Abbey. There he found that a class of the beastliest boys could be kept quiet till break by offering a prize of half a crown for the longest essay, irrespective of all possible merit. Now read on:

“Sir”, remarked Clutterbuck after break, “I claim the prize”.

“But you”, Paul protested feebly, “have written only one-third as many words as Ponsonby, one-fifth as many as Briggs and one-eighth as many as Tangent”.

“Nonetheless, Sir, Dr Fagan would certainly wish me to have the prize”.

And so it proved. You might also like to know that the oldest of these four boys wrote 2222 more words than the second oldest and used more full stops in his essay than any of them who wrote less words than the youngest.

Where was Clutterbuck in the order of age, and how many words did he write?

[tantalizer465]

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If Clutterbuck’s word count is C, then the other word counts are: P=3C, B=5C, T=8C.

And the oldest wrote 2222 more words than the second oldest so, we have one of the following situations:

The only viable solutions are:

or:

So the answer to the second part of the puzzle is that Clutterbuck wrote 1111 words.

To answer the first part we need to interpret:

In the absence of any further information about the number of full stops written by any of the other boys, I think the most reasonable interpretation is:

Condition (b) means that the oldest boy

cannothave written fewer words than the youngest boy, otherwise he would have to have used more full stops than himself. A situation which we cannot satisfy.However condition (a) eliminates [2b], and condition (b) eliminates [1a], [1b], [2a], so together they leave no viable solutions.

A more relaxed interpretation of the sentence would be:

Again this means that the oldest boy

cannothave written fewer words than the youngest boy, and so eliminates cases [1a], [1b], [2a].For [2b] there are no other boys who wrote fewer words than they youngest boy, and the convention for

universal quantificationover the empty set is that it isvacuously true, so in this interpretation we have a single answer:If this is the interpretation the setter wanted us to use it would have been better (and more simply) phrased as:

Here is a Python program that uses this interpretation. It runs in 42ms.

Run:[ @repl.it ]Solution:Clutterbuck is the youngest. He wrote 1111 words.This is indeed the published solution and the explanatory text says:

I don’t see how the sentence [*] is equivalent to “the oldest wrote more than two others”.

Congratulations, Jim, on your interpretation of wording that appears to be deliberately obscure.

In any case, grammar requires that one write fewer words, not “less words”. Words are discrete and countable objects, not something that is measured by the kilogram or the litre.

Is the distinction too subtle for New Scientist?