While working on part two of the Pointless article, I wandered over to Twitter and stumbled upon the following problem:

Can a perfect square ever consist of the same string of digits written out twice (such as in 978978 or 46024602)? cc @jamestanton

— Matt Enlow (@CmonMattTHINK) December 4, 2014

This caught my imagination and I did a bit of an investigation. The results were unexpectedly interesting, involving a connection to a mysterious problem at the cutting edge of number theory and a trip off into the numerical stratosphere in search of some fairly large solutions.

You can read my account of the problem here. The maths used here is probably about first year undergraduate level, and the style is certainly more technical than the *Pointless* article, so come prepared.