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Determine the maximum height a typical egg can fall from without breaking itself. How does the result change if you wrap the egg in some protective material which is not thicker than 5$\;\mathrm{mm}?$ Try couple of different materials.

• Dr. Nec.

There are two ways to measure the amount of wood in a pile of trees. Either as the volume of pure wood in the pile or as the volume of wood together with the empty spaces in the pile. Find the conversion factor between these two units assuming the trees are cylinders of radius $r$ that are layed one on top of the others.

• Bubbles.

A spherical cap of radius $r$ is made by blowing air into a circular surface of soap water. Estimate the velocity of air molecules hitting the surface?

• Jakub's breakfast

Every morning Jakub enjoys his favourite cereals which he pours into a bowl of milk. Assume the bowl is of circulur frustum shape with upper and lower radius $R$ and $r$ respectively ($R$ \geq r$)$, that the cereals are little solid spheres and that before he puts the cereals into the bowl there is milk of height $h$. What is the maximum amount of cereals he can fit into the bowl? You also know that the fraction of volume the cereals occupy inside a fully filled box is $\kappa$.

• Magnetic monopole

Let's have a metal plate magnetized in such a way that the upper and lower sides are the north and south poles respectively. We use these plates to create two semispheres with the outer side being the north pole. Now, if we glue these two semispheres together, we effectively get a magnetic monopole, which, as we know, can not exist in our world. Where did we go wrong?

John is standing on the top of the Žižkov Tower and looks into the windows of neighbouring houses. All the windows face the tower, are of same size and are at the same height. Calculate the radius of the lowest privacy in the houses with such windows. John does not have any binoculars.

One of organizers of Fykos was travelling by train back home. The train was locked in by a snow storm. He was bravely counting snow flakes behind the window and was thinking: „How many snow flakes are in 1kg of snow?“ Are you able to make qualified guess to this question?

If you play any musical instrument, then sometimes you experience problems with rhythm. Define an experiment and measure which frequency (knocking onto a table, pushing piano keys etc.) is easiest to keep. Is there any correlation between other natural effects?

Information system in Prague underground has following feature: during scrolling text on the display to the left, the letters are tilted. Is there a simple way how to do this function on „hardware“ level? What effect will have this at text scrolling in vertical direction? Assume, that information display consists from LEDs spaced in orthogonal grid.

Assume a straight optical fibre. The incoming light enters fibre at maximum angle $α$ from the axis of fibre (higher angles will not be guided by fibre). What is the minimum length of the light pulse to guarantee no overlap between 0 and 1 bit (e.g. at least for short interval the intensity of signal must be minimal or maximal). The length of fibre is $d$.

It is known, that the ice subjected to higher pressure has lower melting temperature. This effect is used also during ice skating. Is this effect strong enough at extremely low temperatures (e.g. is pressure from skate big enough to melt the ice)? If not, what is causing sliding?

Titan (a satellite of Saturn) is very cold (surface temperature is approximately 94 K) and has bulky nitrogen atmosphere, icy surface with lakes made from hydrocarbons. Radar on Cassini probe orbiting Titan found, that objects on the surface rotate faster then the moon itself (approximately by 0$,36°\;\mathrm{year}^{-1})$. Scientific explanation is, that the icy layer on the surface of oceans is affected by a wind. The assumption about moon rotation is, that it is synchronised with orbiting around Saturn

Another hint for existence of under-surface ocean was given by Huygens probe, which landed on the moon surface. During the descent it measured strong electromagnetic waves at frequency approximately 36 Hz. Such waves are amplified at the interface between e.g. water and ice under the surface.

Suggest some methods, to confirm or disprove the existence of hidden ocean on Titan.