While I agree "using tools that solved the problems already is kind of pointless", I don't see anythign wrong with attacking algorithmic problems with say, just the standard Perl installation
It depends on what kind of algorithmic problems your problem
is about. If it's a parsing problem, there's a gigantic
difference between using Pascal and Perl. The former will
force the programmer to make an algorithm. The latter only
needs a few buttons to be pushed. If the problem asks for
complex matrix manipulation, it's going to be a lot easier
in APL than in C.
If you want to focus on solving algorithms, you let everyone
use the same language, or set of languages, and you pick
reasonably 'bare-bone' languages, like Pascal and C. You
don't pick Perl, Python, or APL.