In the US, it is customary to record the date as follows: the number of the month, then the number of the day and then the year. In Europe, the number comes first, then the month and then the year. How many days are there in the year, the date of which can be read definitively, without knowing how it was written?
A pedestrian walked along six streets of one city, passing each street exactly twice, but could not get around them, having passed each one only once. Could this be?
a) In how many ways can Dima paint five Christmas trees in silver, green and blue colours, if the amount of paint is unlimited, and he paints each tree in only one colour?
b) Dima has five baubles: a red, a green, a yellow, a blue and a gold one. In how many ways can he decorate five Christmas trees with them, if he needs to put exactly one bauble on each tree?
c) What about if he can hang several baubles on one Christmas tree (and all of the baubles have to be used)?
Each cell of a \(2 \times 2\) square can be painted either black or white. How many different patterns can be obtained?
How many ways can Rob fill in one card in the “Sport Forecast” lottery? (In this lottery, you need to predict the outcomes of thirteen sports matches. The result of each match is the victory of one of the teams or a draw, and the scores do not play a role).
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?
There are five books on a shelf. In how many ways can the books be arranged in a stack. (Stacks may consist of any number of books)?
\(N\) young men and \(N\) young ladies gathered on the dance floor. How many ways can they split into pairs in order to participate in the next dance?
Between the nine planets of the solar system, a cosmic messaging system is introduced. Rockets fly along the following routes: Earth – Mercury, Pluto – Venus, Earth – Pluto, Pluto – Mercury, Mercury – Venus, Uranus – Neptune, Neptune – Saturn, Saturn – Jupiter, Jupiter – Mars and Mars – Uranus. Is it possible to get from Earth to Mars?
There are 9 cities in the country Number with the names 1, 2, 3, 4, 5, 6, 7, 8, 9. The traveller discovered that two cities are connected by an airline if and only if a two-digit number made up of the digit-names of these cities, is divisible by 3. Is it possible to get from city 1 to city 9?