Any rectangle can be cut into squares if the squares don't have to be the same size.Or it can't. Now I have not seen a really good proof either way (I have thrown it about on Twitter with Adam Creen and James Grime who both made interesting contributions to my thinking). Any thoughts? Adam and James both mentioned irrationals though I am not yet convinced that even a rectangle in the ratio1:root 2 could not be cut. So what do you think? Sorry 'AJs' Conjecture' isn't curriculum maths, it just interests me, and I am curious that I cannot find this as a theorem out there anywhere. It seems such a basic thing to want to find out! And could it be used with A-level students or top-set GCSE ones?