Fred and George are twin brothers. One of them always tells the truth, and the other always lies. You can ask only one question to one of the brothers, to which he will answer “yes” or “no”. Try to find out the name of each of the twins.
Harry, Jack and Fred were seated so that Harry could see Jack and Fred, Jack could only see Fred, and Fred could not see anyone. Then, from a bag which contained two white caps and three black caps (the contents of the bag were known to the boys), they took out and each put on a cap of an unknown color, and the other two hats remained in the sack. Harry said that he could not determine the color of his hat. Jack heard Harry’s statement and said that he did not have enough information to determine the color of his hat. Could Fred on the basis of these answers determine the color of his cap?
Three friends – Peter, Ryan and Sarah – are university students, each studying a different subject from one of the following: mathematics, physics or chemistry. If Peter is the mathematician then Sarah isn’t the physicist. If Ryan isn’t the physicist then Peter is the mathematician. If Sarah isn’t the mathematician then Ryan is the chemist. Can you determine which subject each of the friends is studying?
At the cat show, 10 male cats and 19 female cats sit in a row where next to each female cat sits a fatter male cat. Prove that next to each male cat is a female cat, which is thinner than it.
The vendor has a cup weighing scales with unequal shoulders and weights. First he weighs the goods on one cup, then on the other, and takes the average weight. Does he deceive customers?
We meet three people: Alex, Brian and Ben. One of them is an architect, the other is a baker and the third is an bus driver. One lives in Aberdeen, the other in Birmingham and the third in Brighton.
1) Ben is in Birmingham only for trips, and even then very rarely. However, all his relatives live in this city.
2) For two of these people the first letter of their name, the city they live in and their job is the same.
3) The wife of the architect is Ben’s younger sister.
Professions of family members. In the Smith family there are 5 people: a husband, a wife, their son, a husband’s sister and the father of his wife. They all work. One is an engineer, another is a lawyer, the third is a mechanic, the fourth is an economist, the fifth is a teacher. Here’s what else is known about them. The lawyer and the teacher are not blood relatives. The mechanic is a good athlete. He followed in the footsteps of an economist and played football for the national team of the plant. The engineer is older than his brother’s wife, but younger than the teacher. The economist is older than the mechanic. What are the professions of each member of the Smith family?
Burbot-Liman. Find the numbers that, when substituted for letters instead of the letters in the expression \(NALIM \times 4 = LIMAN\), fulfill the given equality (different letters correspond to different numbers, but identical letters correspond to identical numbers)
This problem is from Ancient Rome.
A rich senator died, leaving his wife pregnant. After the senator’s death it was found out that he left a property of 210 talents (an Ancient Roman currency) in his will as follows: “In the case of the birth of a son, give the boy two thirds of my property (i.e. 140 talents) and the other third (i.e. 70 talents) to the mother. In the case of the birth of a daughter, give the girl one third of my property (i.e. 70 talents) and the other two thirds (i.e. 140 talents) to the mother.”
The senator’s widow gave birth to twins: one boy and one girl. This possibility was not foreseen by the late senator. How can the property be divided between three inheritors so that it is as close as possible to the instructions of the will?
In a race between 6 athletes, Andrew falls behind Boris and two athletes finish between them. Vincent finished after Declan, but before George. Declan finished before Boris but after Eric. Which order did the athletes finish the race in?