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What's the difference between a puzzle and a maths question?

Something to do with humour and surprise, perhaps?

What's the difference between a puzzle and a maths question?  For some people there is a clear difference: puzzles are things that you do for fun, maths questions are something you do to test your maths (problem solving) skills.  But defining the boundary between 'fun' and 'testing maths skills' is very subjective. No two people draw the boundary in the same place.

In my late teens and early twenties I was one of the puzzle setters for New Scientist magazine*, and part of my role was to act as a referee for other people's puzzles before they were published.

There were some 'puzzles' that were submitted that didn't feel like puzzles at all.  I began to identify the features that I felt were needed to make something a puzzle.

I came up with three. 

(a) An intriguing or amusing question, maybe because it seems at first as if there isn't enough information to answer it.

(b) An aha moment when solving it (where you realise you've been looking at the problem the wrong way, have a moment of insight, or discover a neat shortcut that takes you rapidly to the answer).  

(c) An amusing or surprising twist in the answer.  Perhaps the answer spells out an interesting word, or is a number with a nice pattern.  Or you fell into a trap and got the answer wrong (and kick yourself).  

I concluded that if a so-called puzzle has none of the above qualities then it doesn't count as a puzzle at all, it is a mathematical exercise.

I was reminded of this recently when looking through the archive of puzzles from the BBC's Today programme, a daily feature that started a couple of months ago.

There are some nice puzzles in there.  For example I like No.28 One for Halloween Lovers (for its simple everydayness), and No.47 What Links The Countries?  (because it combines pattern spotting with a bit of general knowledge).

But I am surprised that some of the other challenges made it through the editor's filter.  For example, puzzle no.24 is a so-called cryptarithm, a sum in which the digits have been replaced by letters.  The puzzle asks you to find how many different solutions there are to the sum: BBC + NEWS = JOHN

If you have time to spare maybe you'll find all the possible solutions. But that's unlikely, because there are apparently 96 of them.  

That question fails on all three of my criteria, and to me that means it is not a puzzle, not really even a maths question, it's just a chore. 


POSTSCRIPT:  Since I wrote this blog, I've continued to keep tabs on the Today programme's daily 'puzzle'.  Occasionally I read out the day's question to my family and ask them: 'Is this a puzzle or a maths question?'.  They are usually unanimous in voting one way or the other.  They far prefer the ones that they describe as puzzles. 

If you are a maths teacher doing a 'puzzle' challenge, you can do a similar survey - not by asking your students, but by asking teachers from other departments.  Show the question to the Head of English and ask them: 'Is this a puzzle or a maths question?'.  You might find their response illuminating, not least because if their response is 'puzzle', that's often a sign that it's something that is more likely to engage them.

* This blog prompted New Scientist magazine to contact me, and in 2019 the magazine introduced a new puzzle column for which I have been acting as adviser and an informal editor.  The New Scientist puzzle column adheres to the principles discussed in this blog.