Jessica, Nicole and Alex received 6 coins between them: 3 gold coins and 3 silver coins. Each of them received 2 coins. Jessica doesn’t know which coins the others received but only which coins she has. Think of a question which Jessica can answer with either “yes”, “no” or “I don’t know” such that from the answer you can know which coins Jessica has.
A space traveller decided to visit the planet and upon arrival he met three inhabitants. The traveller asked each of the inhabitants: “How many truth tellers are there among your companions?”. The first one answered: “None.” The second one said: “One”. What did the third alien say?
The king made a test for the future groom of his daughter. He put the princess in one of three rooms, a tiger in the other, and left the last room empty. It is known that the sign on the door where the princess is sitting is true, where the tiger is – it is false, and nothing is known about the sign on the third room. The tablets are as follows:
1 – room 3 is empty
2 – the tiger is in room 1
3 – this room is empty
Can the prince correctly guess the room with the princess?
On Brennan’s birthday, the postman Daniel wants to find out how old Brennan is. Sarah says that Brennan is over 11 years old, and Matt claims that he is more than 10 years old. How old is Brennan, if it is known that exactly one of them was mistaken? Justify your answer.
There are \(12\) aliens in the High Council of the planet of liars and truth tellers. “There is no-one honest here,” said the first member of the council. “There is at most one honest person here,” said the second person. The third person said that there are at most \(2\) honest members, the fourth person said there are at most \(3\) honest aliens, and so on until the twelfth person, who said there are at most \(11\) honest aliens. How many honest members are in the High Council?
Sarah believes that two watermelons are heavier than three melons, Anna believes that three watermelons are heavier than four melons. It is known that one of the girls is right, and the other is mistaken. Is it true that 12 watermelons are heavier than 18 melons? (It is believed that all watermelons weigh the same and all melons weigh the same.)
One day all the truth tellers on the planet decided to carry a clearly visible mark of truth in order to be distinguished from liars. Two truth tellers and two liars met and looked at each other. Which of them could say the phrase:
“All of us are truth tellers.”
“Only one of you is a truth teller.”
“Exactly two of you are truth tellers.”
In Neverland, only elves and gnomes live. Gnomes lie about their gold, but in any other instances they tell the truth. Elves lie when talking about gnomes, but in other instances they tell the truth. One day two neverlandians said:
\(A\): All my gold I stole from the Dragon.
\(B\): You’re lying.
Determine whether each of them is an elf or a gnome.
In the king’s prison, there are five cells numbered from 1 to 5. In each cell, there is one prisoner. Kristen persuaded the king to conduct an experiment: on the wall of each cell she writes at one point a number and at midnight, each prisoner will go to the cell with the indicated number (if the number on the wall coincides with the cell number, the prisoner does not go anywhere). On the following night at midnight, the prisoners again must move from their cell to another cell according to the instructions on the wall, and they do this for five nights. If the location of prisoners in the cells for all six days (including the first) is never repeated, then Kristen will be given the title of Wisdom, and the prisoners will be released. Help Kristen write numbers in the cells.
One day, Claudia, Sofia and Freia noticed that they brought the same toy cars to kindergarten. Claudia has a car with a trailer, a small car and a green car without a trailer. Sofia has a car without a trailer and a small green one with a trailer, and Freia has a big car and a small blue car with a trailer. What kind of car (in terms of colour, size and availability of a trailer) did all of the girls bring to the kindergarten? Explain the answer.