Four children said the following about each other.
Mary: Sarah, Nathan and George solved the problem.
Sarah: Mary, Nathan and George didn’t solve the problem.
Nathan: Mary and Sarah lied.
George: Mary, Sarah and Nathan told the truth.
How many of the children actually told the truth?
James spent the first Tuesday of some month in Liverpool and the first Tuesday after the first Monday he spent in Newcastle. In the next month, James spent the first Tuesday in Dover and the first Tuesday after the first Monday he spent in Bristol. Could you determine the dates (day and month) spent by James in each of the cities?
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?
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?
An investigation is being conducted into the case of a stolen mustang. There are three suspects – Bill, Joe and Sam. At the trial, Sam said that the mustang was stolen by Joe. Bill and Joe also testified, but what they said, no one remembered, and all the records were lost. In the course of the trial it became clear that only one of the defendants had stolen the Mustang, and that only he had given a truthful testimony. So who stole the mustang?
In a vase, there is a bouquet of 7 white and blue lilac branches. It is known that 1) at least one branch is white, 2) out of any two branches, at least one is blue. How many white branches and how many blue are there in the bouquet?
In Conrad’s collection there are four royal gold five-pound coins. Conrad was told that some two of them were fake. Conrad wants to check (prove or disprove) that among the coins there are exactly two fake ones. Will he be able to do this with the help of two weighings on weighing scales without weights? (Counterfeit coins are the same in weight, real ones are also the same in weight, but false ones are lighter than real ones.)
Janine and Zahara each thought of a natural number and said them to Alex. Alex wrote the sum of the thought of numbers onto one sheet of paper, and on the other – their product, after which one of the sheets was hidden, and the other (on it was written the number of 2002) was shown to Janine and Zahara. Seeing this number, Janine said that she did not know what number Zahara had thought of. Hearing this, Zahara said that she did not know what number Janine had thought of. What was the number which Zahara had thought of?