There are two purses and one coin. Inside the first purse is one coin, and inside the second purse is one coin. How can this be?
A message is encrypted by replacing the letters of the source text with pairs of digits according to some table (known only to the sender and receiver) in which different letters of the alphabet correspond to different pairs of digits. The cryptographer was given the task to restore the encrypted text. In which case will it be easier for him to perform the task: if it is known that the first word of the second line is a “thermometer” or that the first word of the third line is “smother”? Justify your answer. (It is assumed that the cryptographic table is not known).
Andrew drives his car at a speed of 60 km/h. He wants to travel every kilometre 1 minute faster. By how much should he increase his speed?
Find the coefficient of \(x\) for the polynomial \((x - a) (x - b) (x - c) \dots (x - z)\).
In a room, there are three-legged stools and four-legged chairs. When people sat down on all of these seats, there were 39 legs (human and stool/chair legs) in the room. How many stools are there in the room?
Everyone believed that the Dragon was one-eyed, two-eared, three-legged, four-nosed and five-headed. In fact, only four of these definitions form a certain pattern, and one is redundant. Which characteristic is unnecessary?
Jemima always tells the truth, but when she was asked the same question twice, she gave different answers. What kind of question could this be?
In a purse, there are 2 coins which make a total of 15 pence. One of them is not a five pence coin. What kind of coins are these?
What is there a greater number of: cats, except for those cats that are not named Fluffy, or animals named Fluffy, except for those that are not cats?
The angle at the top of a crane is \(20^{\circ}\). How will the magnitude of this angle change when looking at the crane with binoculars which triple the size of everything?