Problems

If you are on a boat and toss a suitcase overboard, will the water level rise or fall?

Due to the mistake in the bakery the cake that was supposed to be shaped as two concentric pieces came out as the left side of picture. Find the smallest amount of pieces the cake should be cut in, to build the cake on the right side of picture.

Find all such \(n\), that the closed system of \(n\) gears on a plane can move. We call a system closed if the first gear wheel is connected to the second and the \(n\)th, the second is connected to the first and the third, and so on. On the picture we have a closed system of three gears.