A monkey, donkey and goat decided to play a game. They sat in a row, with the monkey on the right. They started to play the violin, but very poorly. They changed places and then the donkey was in the middle. However the violin trio still didn’t sound as they wanted it to. They changed places once more. After changing places 3 times, each of the three “musicians” had a chance to sit in the left, middle and right of the row. Who sat where after the third change of seats?
There is a group of 5 people: Alex, Beatrice, Victor, Gregory and Deborah. Each of them has one of the following codenames: V, W, X, Y, Z. We know that:
Alex is 1 year older than V,
Beatrice is 2 years older than W,
Victor is 3 years older than X,
Gregory is 4 years older than Y.
Who is older and by how much: Deborah or Z?
Going to school, Michael found everything he needed under the pillow, under the sofa, on the table or under the table. The items he needed to find were a notebook, a cheat sheet, an mp3 player and sneakers. Under the table, he did not find a notebook or an mp3 player. His cheat sheet never lies on the floor. The mp3 player was neither on the table nor under the sofa. What was lying where, if there was only one object in each of the places?
Some inhabitants of the Island of Multi-coloured Frogs speak only the truth, and the rest always lie. Three islanders said:
Bree: There are no blue frogs on our island.
Kevin: Bree is a liar. She herself is a blue frog!
Clara: Of course, Bree is a liar. But she’s a red frog.
Are there any blue frogs on this island?
In the family of happy gnomes there is a father, a mother and a child. The names of the family members: Alex, Charlie and Jo. At the dinner table two gnomes made two statements.
Charlie said: “Alex and Jo are of different genders. Alex and Charlie are my parents”.
Alex said: “I am Jo’s father. I am the daughter of Charlie”.
Who is who? That is, what is the name of the father, the mother and the child, if it is known that each gnome lied once, and each told the truth once.
On the first day of school, in all three of the first year classes (1A, 1B, 1C), there were three lessons: Maths, French and Biology. Two classes cannot have the same lesson at the same time. 1B’s first lesson was Maths. The Biology teacher praised the students in 1B: “You have even better marks than 1A”. 1A’s second lesson was not French. Which class’s last lesson was Biology?
Imogen’s cat always sneezes before it rains. Today the cat sneezed. “So, it will rain” thinks Imogen. Is she right?
Three tortoises crawl along the road in a line. “Two tortoises are crawling behind me,” says the first. “One tortoise is crawling behind me, and one tortoise is crawling in front of me,” says the second. “Two tortoises are crawling in front of me, and one tortoise is crawling behind me,” says the third. How can this be?
Three wise men ride on a train. Suddenly the train drives into a tunnel, and after the lights come on, each of the men sees that the faces of his colleagues are stained with soot that has flown through the car window. All three begin to laugh at their stained companions, but suddenly the most intelligent man guesses that his face is also stained. How did he do it?
In each cell of a \(25 \times 25\) square table, one of the numbers 1, 2, 3, ..., 25 is written. In cells, that are symmetric relative to the main diagonal, equal numbers are written. There are no two equal numbers in any row and in any column. Prove that the numbers on the main diagonal are pairwise distinct.