In front of a gnome there lie three piles of diamonds: one with 17, one with 21 and one with 27 diamonds. In one of the piles lies one fake diamond. All the diamonds have the same appearance, and all real diamonds weigh the same, and the fake one differs in its weight. The gnome has a cup weighing scale without weights. The dwarf must find with one weighing a pile, in which all the diamonds are real. How should he do it?
Ladybirds gathered in a sunny clearing. If the ladybird has \(6\) spots, then it always speaks the truth, and if it has \(4\) spots, then it always lies. There are no other types of ladybirds in the meadow. The first ladybird said: “We each have the same number of spots on our backs.” The second one said: “Everyone has \(30\) spots on their backs in total.” “No, we all have \(26\) spots on their backs in total,” the third objected. “Of these three, exactly one told the truth,” – said each of the other ladybirds. How many ladybugs were gathered in the meadow?
Thirty girls – 13 in red dresses and 17 in blue dresses – led a dance around the Christmas tree. Subsequently, each of them was asked if her neighbour on the right was in a blue dress. It turned out that those girls which answered correctly were only those who stood between two girls in dresses of the same color. How many girls could have said yes?
Here’s a rather simple rebus:
\(EX\) is four times larger than \(OJ\).
\(AJ\) is four times larger than \(OX\).
Find the sum of all four numbers.
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?
11 scouts are working on 5 different badges. Prove that there will be two scouts \(A\) and \(B\), such that every badge that \(A\) is working towards is also being worked towards by \(B\).
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?