thanks Hugo, the 1/3+2/3 was an example of the mathematics not the problem. Clumsy I know but fuel for the pedants!

I agree here. You shouldn't exclude the 16 solutions with repeating decimals.

They are all cases where denominator is 3 e.g 1/3+2/3 = 1 exactly so obviously 0.333'+0.666'=1 exactly.

On...