Busy-Beaver-like question for WHILE-Programs (Theoretical CS)
Use the same proof as Radó did in his paper: Assume there is a program $\Sigma$ that computes the value asked for, combine with a program that given $n$ computes $2 n$, and add $1$ to the result. Call the number of lines of the result $N$. Writing a program that computes $N$ should take at most $N$ lines (add $1$ $N$ times). Combine the above, the result is of length $2 N$ and computes a value larger than the largest it is able to compute given it's length. Contradiction, $\Sigma$ can't exist.