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.

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    $\begingroup$ Mental Calculation World Cup and Rüdiger Gamm for motivation.. $\endgroup$ – Git Gud Apr 28 '16 at 21:55
  • $\begingroup$ I think that hand calculations are a wonderful change from calculator calculations in a math competition. Would be a good idea in my opinion. Or perhaps you would have to produce an algorithm/series or something that has the fastest convergence for a problem? To make up for those who can't think calculations as fast as others. $\endgroup$ – Simply Beautiful Art Apr 28 '16 at 21:55
  • $\begingroup$ I'm not aware of any math competitions that allow the use of calculators. Can you point me at some, @SimpleArt (so that I know to steer clear - the calculators are an abomination in competitions IMHO :-) $\endgroup$ – Jyrki Lahtonen Apr 28 '16 at 21:58
  • $\begingroup$ @JyrkiLahtonen Actually, I don't really know any math competitions myself. I just think non-calculator competitions would be fun. $\endgroup$ – Simply Beautiful Art Apr 28 '16 at 22:00

Yes. Take a look at Flash Anzan competitions in Japan.

Basically, you are given $15$ numbers, each between $100$ and $999$. The numbers are shown for a total of $2$ seconds. You must then give the sum of the numbers in the next second.

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    $\begingroup$ That's not exactly what I meant. Fast mental calculations are a special skill. I meant pen and paper calculations, with the use of different methods $\endgroup$ – Yuriy S Apr 28 '16 at 22:08
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    $\begingroup$ Besides, going by your link, it's for kids. I indicated college level $\endgroup$ – Yuriy S Apr 28 '16 at 22:11

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