> However, one does not simply email a CV to them. This is HMG, after all! 
> You must fill in a long, complex online application form. And some of the 
> fields really aren't very clearly labelled.

And then watch out, they often interview someone who knows you, just to 
check certain things...

> Any remotely complex problems I might have solved have been solved by me 
> and me alone.

Scale back a bit on your definition of "complex" then.  How about "the most 
complex problem that you have solved with the aid of others"?  You must have 
done something where you needed to ask someone else for advice/help - or 
where you provided assistance to some other people working on a larger 
problem?

> Or should I write something about the time when I tried to build a parser 
> for my computer-aided algebra system, and ended up inventing Dijkstra's 
> shunting algorithm?

Yes, I suspect they would like that.  They are after evidence, evidence that 
you would be a useful person working for them.  Things like that show that 
even though your current job doesn't require it, you are interested enough 
in such concepts to spend time on them.

> 4. Please describe a time when you took on a task that illustrates your 
> active interest in this area of work and allowed you to develop new 
> skills.
>
> Uuuhhhh... Well I can tell you all mannar of things I've learned out of 
> pure curiosity. But things I learned because of attempting to perform a 
> specific "task"?

Same sort of thing as the previous answer would do.  But I guess it should 
try to be related to whatever job you are applying for.  I'm sure you can 
wangle something.

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