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(10 points)1. Series 33. Year - P. planet destroyer

How small could a weapon capable of destroying a planet be? We are interested in the smallest and the lightest such weapons. The process should be reasonably fast, at least shorter than a human lifetime, and the faster it is, the better.

(10 points)1. Series 33. Year - S. slow start-up

(3 points)5. Series 32. Year - 2. warm reachability into the ball

Imagine you have subcooled homogeneous metal ball that you have just taken out of a freezer set to very low temperature. You want to find out how fast the ball temperature will increase if you put it in a warm room. It would be a university-level problem. Because of that, we made it easier for you. We ask about how deep into the ball will the „warm area“ reach. You can estimate it using dimensional analysis. We know relevant parameters of the ball - its density $\left [ \rho \right ] = \jd {kg.m^{-3}}$, specific heat capacity $\left [c\right ] = \jd {J.kg^{-1}.K^{-1}}$, thermal conductivity of the ball $\left [ \lambda \right ] = \jd {W.m^{-1}.K^{-1}}$ and we are interested in dependence on time $\left [t\right ] = \jd {s}$.

Karel inspired himself by a problem from Eötvös Competition.

(10 points)6. Series 31. Year - S. Matrices and populations

Mirek and Lukáš fill matrices with atto-foxes.

(9 points)5. Series 31. Year - P. floating mercury

Try to invent as much „physics tricks“ as possible thanks to which mercury would float on the liquid water for at least a limited time. The more permanent solution you find, the better.

(10 points)5. Series 31. Year - S. Differential equations are growing well

Mirek and Lukáš have already grown their algebra, now they have different seeds.

(8 points)3. Series 31. Year - P. folded paper

Everyone has certainly heard and surely tried it: „Sheet of paper can not be folded in a half more than seven times.“ Is it really true? Find boundary conditions.

Kuba was bored and folded a paper.

(10 points)3. Series 31. Year - S. going for a walk with integrals

We are sorry, this task is not yet translated…

Mirek and Lukáš random-walk to school.

(3 points)2. Series 31. Year - 1. Tooth Fairy

How big would the storage facilities of the Tooth Fairy need to be, to store all of the primary teeth of all of the children of the world? Or, in other words, how rapidly would they need to grow? How long would it take for the whole Earth supply of phosphorous to be contained in those storage facilities?

Karel's mind wandered to the Discworld

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