Dear Uncle Colin,

Why do you insist on giving smart-arse answers to simple puzzles on Twitter?

- Malice Establishes Almost Nothing

Hi, MEAN, and thanks for your message!

First up, please don’t confuse my cheerful ragging of questions with malice; on the contrary, coming up with alternative approaches, unexpected ways of tackling things, different ideas is exactly what maths is meant to be about, isn’t it?

There are three kinds of maths questions I typically see on Twitter.

There are the glorious Good Puzzles, the sort of thing that @cshearer41 and @edsouthall are renowned for, ones where the pleasure is in the journey to the solution rather than the solution itself. Those, I tend to engage with keenly and in a spirit of trying to find the answer from The Book.

Then there are the bloody stupid ones that do the rounds on Facebook and typically claim that 98% will fail. Those, I roll my eyes at and ignore (or possibly tell people off for posting.)

And there’s a third category, that sits somewhere in between. (For example, “make 100 from the digits 9999, using only two mathematical operations.”) There’s an expected solution to that which I’ll spoiler in a footnote ((99 + 9/9)), but that feels like a bit of a dead-end to me. Spot a solution and stop? No. The end is not the end.

I love open-ended puzzles as much as the Good Puzzles I mentioned earlier. And if I encounter a closed puzzle, I try to open it up. Can I do it in no operations? ($99.9\dot9$). How about unexpected operations? ($\frac{99}{99%}$, or $$99 + \nCr{9}{9}$$). Or a factorial? ($\frac{\left(9 + (\sqrt{9})!\right)\sqrt{9}!}{.9}$). $\ceil{\sqrt{9999}}$ works, as does $\floor{\frac{99}{\sqrt[9]{.9}}}$.

There’s more than one way to do it, and showing some of the more creative ways hopefully reminds people that there’s more to maths than “the correct answer”.

Hope that helps!

- Uncle Colin