A very rich lady goes with a bag of coins (not more than 400) to the city. In the city she meets four vagabonds. She gives the first vagabond 4 coins and a quarter of the number of coins which is left in the bag. She applies the same procedure to the second, third and fourth vagabond (so division by 4 worked always). With how many coins did she leave home?

A long and straight row of soldiers is marching with constant speed. The dog of the commander runs along the row from the end till the beginning, from the beginning till the end, from the end till the beginning etc. This takes always 2 minutes, 1 minute, 2 minutes, etc.
At some point the soldiers have to pass a very small bridge. However, the commander does not trust the strength bridge completely. He wonders how much time it will take them to pass the bridge when they stay marching with the same speed. How much time is that?

At the same time a block of iron and an equally heavy iron sphere are released from the top of a slope. Assume that the friction between the slope has a negligible effect on the velocity of the block and the sphere. Which of the two will be down first?