Three tortoises crawl along the road in a line. “Two tortoises are crawling behind me,” says the first. “One tortoise is crawling behind me, and one tortoise is crawling in front of me,” says the second. “Two tortoises are crawling in front of me, and one tortoise is crawling behind me,” says the third. How can this be?
Is it possible to fill a \(5 \times 5\) board with \(1 \times 2\) dominoes?
a) An axisymmetric convex 101-gon is given. Prove that its axis of symmetry passes through one of its vertices.
b) What can be said about the case of a decagon?
A coin is tossed three times. How many different sequences of heads and tails can you get?
Each cell of a \(2 \times 2\) square can be painted either black or white. How many different patterns can be obtained?
In a football team (made up of 11 people), a captain and his deputy need to be chosen. How many ways can this be done?
If a salary is first increased by 20%, and then reduced by 20%, will the salary paid increase or decrease as a result?
Arrange in a row the numbers from 1 to 100 so that any two neighbouring ones differ by at least 50.
The numbers from 1 to 9999 are written out in a row. How can I remove 100 digits from this row so that the remaining number is a) maximal b) minimal?
A group of 20 tourists go on a trip. The oldest member of the group is 35, the youngest is 20. Is it true that there are members of the group that are the same age?