Solve the equation \(xy = x + y\) in integers.
Two people had two square cakes. Each person made 2 straight cuts from edge to edge on their cake. After doing this, one person ended up with three pieces, and the other with four. How could this be?
Try to find all natural numbers which are five times greater than their last digit.
In an apartment building in which there are only married couples with children, a population census was carried out. The person who conducted the census stated in the report: “There are more adults in the building than children. Each boy has a sister and there are more boys than girls. There are no childless families.” This report was incorrect. Why?
On a table five coins are placed in a row: the middle coin shows heads and the rest show tails. It is allowed to turn over three adjacent coins simultaneously. Is it possible to get all five coins to show heads after turning the coins over several times?
Before the start of the Olympics, the price of hockey pucks went up by 10%, and after the end of the Olympics they fell by 10%.
When were the pucks more expensive – before the price rise or after the fall?
Pinocchio and Pierrot were racing. Pierrot ran the entire race at the same speed, and Pinocchio ran half the way two times faster than Pierrot, and the second half twice as slow as Pierrot. Who won the race?
Jack and Ben had a bicycle on which they went to a neighborhood village. They rode it in turns, but whenever one rode, the other walked and did not run. They managed to arrive in the village at the same time and almost twice as fast than if they had both walked. How did they do it?
Try to make a square from a set of rods:
6 rods of length 1 cm, 3 rods of length 2 cm each, 6 rods of length 3 cm and 5 rods of length 4 cm. You are not able to break the rods or place them on top of one another.
Find a two-digit number that is 5 times the sum of its digits.