Is it possible to take a whole number $x$ and produce another whole number $y$ which decimal form would have all digits from $x$ duplicated (e.g. $123 \rightarrow 112233$) using solely arithmetic operations?
This question is inspired by programming questions like this one - the idea is to have an elegant solution which avoids using conversion to a string.
I'm going to say no. The hitch is that $112233=11\cdot10203$, but any function smart enough to do $12\mapsto102$, $123\mapsto10203$, $1234\mapsto1020304$ and so on is going to need a loop in it.
Contrast with making $123123=123\cdot 1001$, which is achievable in a relatively simple function, since $$1001=1+10^{\lfloor\log_{10}123\rfloor+1}$$