The jugs problem - but is it maths?

Some of the other websites I have read about the Jugs problem state that it is merely a riddle, or that there is no maths involved in solving it.  So: are the problems in the previous blog posts (Die Hard: With a Vengeance - 3 and 5 gallon jugs and Generalising the jugs problem) actually mathematics or not?

One reason this is worth considering (in my opinion) is that there are lots of other problems that fall into this category (“nice - but is it maths?”).

Clearly this depends on your definition of “mathematics”.  There are, though, lots of different skills that are used (or that can be used) to solve the problem and these are either clearly mathematical or are helpful in solving other mathematical problems.  I think these include:

·         Flexibility.  Working in different ways (practically, using diagrams, with numbers) is helpful.

·         Using trial and improvement.  Very often we don’t know how to get started.  Getting started by doing something is often useful, even if it turns out not to be correct.

·         Getting used to the problem.  Realising that you can pour from one jug to the other, realising that when you pour away water you are emptying a jug, etc, are all helpful.  It might also be useful to realise that the units involved are all the same, so if gallons are off-putting because of their unfamiliarity then working in pints or litres will give the same answer.

·         Tenacity.  I suppose this follows on from the trial and improvement.

·         Mathematising.  While it is possible to answer the question without doing this, the mathematisation makes it easier to generalise.

Even if it isn’t maths in its original form, a problem like this can end up using lots of mathematical skills. 

So: it is mathematics?  I would say "yes", but if you disagree I would say "who cares?".  There are so many useful things that arise from doing it that it doesn’t really matter!