In the garden of Sandra and Lewis 2006 rose bushes were growing. Lewis watered half of all the bushes, and Sandra watered half of all the bushes. At the same time, it turned out that exactly three bushes, the most beautiful, were watered by both Sandra and Lewis. How many rose bushes have not been watered?
In a class there are 50 children. Some of the children know all the letters except “h” and they miss this letter out when writing. The rest know all the letters except “c” which they also miss out. One day the teacher asked 10 of the pupils to write the word “cat”, 18 other pupils to write “hat” and the rest to write the word “chat”. The words “cat” and “hat” each ended up being written 15 times. How many of the pupils wrote their word correctly?
Peter and 9 other people play such a game: everyone rolls a dice. The player receives a prize if he or she rolled a number that no one else was able to roll.
a) What is the probability that Peter will receive a prize?
b) What is the probability that at least someone will receive a prize?
A cube with side length of 20 is divided into 8000 unit cubes, and on each cube a number is written. It is known that in each column of 20 cubes parallel to the edge of the cube, the sum of the numbers is equal to 1 (the columns in all three directions are considered). On some cubes a number 10 is written. Through this cube there are three layers of \(1 \times 20 \times 20\) cubes, parallel to the faces of the cube. Find the sum of all the numbers outside of these layers.