Carpenters were sawing some logs. They made 10 cuts and this produced 16 pieces of wood. How many logs did they saw?
Among 4 people there are no three with the same name, the same middle name and the same surname, but any two people have either the same first name, middle name or surname. Can this be so?
Several natives of an island met up $($each either a liar or a knight$)$, and everyone said to everyone else: “You are all liars.” How many knights were there among them?
Elephants, rhinoceroses, giraffes. In all zoos where there are elephants and rhinoceroses, there are no giraffes. In all zoos where there are rhinoceroses and there are no giraffes, there are elephants. Finally, in all zoos where there are elephants and giraffes, there are also rhinoceroses. Could there be a zoo in which there are elephants, but there are no giraffes and no rhinoceroses?
So, the mother exclaimed – “It’s a miracle!”, and immediately the mum, dad and the children went to the pet store. “But there are more than fifty bullfinches here, how will we decide?,” the younger brother nearly cried when he saw bullfinches. “Don’t worry,” said the eldest, “there are less than fifty of them”. “The main thing,” said the mother, “is that there is at least one!”. “Yes, it’s funny,” Dad summed up, “of your three phrases, only one corresponds to reality.” Can you say how many bullfinches there was in the store, knowing that they bought the child a bullfinch?
In a basket, there are 30 mushrooms. Among any 12 of them there is at least one brown one, and among any 20 mushrooms, there is at least one chanterelle. How many brown mushrooms and how many chanterelles are there in the basket?
12 mayor candidates talked about themselves. After a while, one said: “The number of lies told me before me was one.” Another said: “And now – two”. “And now – three,” said the third, and so on until the 12th, who said: “And now they lied 12 times.” Then the presenter interrupted the discussion. It turned out that at least one candidate correctly calculated how many lies were told before him. So, how many times have the candidates lied?
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?
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?
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?
One person says: “I’m a liar.” Is he a native of the island of knights and liars?
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?
A bagel is cut into sectors. Ten cuts were made. How many pieces did this make?
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?
Fred always tells the truth, but Vadim always lies. What question should they be asked, so that they would give the same answers?
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?
Some girls are on a street. On the street, standing in a circle, four girls are talking: Janine, Mimi, Beatrix and Tash. A girl in a green dress $($not Janine or Mimi$)$ stands between a girl in a blue dress and Tash. A girl in a white dress is standing between a girl in a pink dress and Mimi. What dress is on each of the girls?
We meet three people: Alex, Brian and Ben. One of them is an architect, the other is a baker and the third is an archeologist. 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.