Most of the people consider hand calculations the thing of the past.
However, I recently started thinking about it and there are many interesting ways to do basic arithmetics on large numbers, factorize, extract roots, solve equations and even compute transcendental functions, most of which can be done by hand if needed.
I know it was a huge thing in the past (especially before the invention of the logarithmic ruler and other tools), but what about now?
Are there any math competitions (college, or at least high-school level) where the participants are expected to do complicated calculations without any tool except pen and paper?
In my opinion, it will be interesting to compare different approaches, and how the usual numerical methods can be optimized for hand calculations.
I do not seek to participate in any such competition myself, but some interesting problems, methods and achieved records would be nice. Thank you!
If not right now, what were the most famous among such competitions in the past?
Edit - Just to clarify: I mean the competitions where high precision calculations are necessary and expected. (As opposed to competitions dedicated to proofs, logic etc.)
Edit 2 - And I don't mean high-speed mental calculations, which is completely different thing.