Each of the islanders gathered in the square said to the others: You are all liars.
How many knights are there among them?

📜 Leaflet #amazing_island

Wikipedia

1) Each of the 7 residents of the island sitting at the round table said: "My neighbors are a liar and a knight."
How many knights and how many liars are sitting at the table?

2) The same question if 9 islanders were sitting at the table?

📜 Leaflet #amazing_island

What question do you have to ask an islander to find out if he has a pet crocodile living in his house?

💡 I remind you that there are knights and liars on the island. Knights always tell the truth and liars always lie.

🎯 Solution:
A question like this:
«If I asked, "Do you have a pet crocodile at home", would you say yes?»

Why:
1) A liar with a crocodile, always lies, would answer "no" to the question "Do you have a pet crocodile at home" and answer "yes" to my question;
2) A liar without a crocodile, similarly, "no."
3) A knight with a crocodile, always tells the truth, so "yes";
4) A knight without a crocodile, similarly, "no".

Bottom line: the resident of the island with a crocodile answers my question "yes", and without a crocodile - "no".

📜 Leaflet #amazing_island

A tribe of cannibals caught Robinson Crusoe. The leader said, "We would be happy to let you go, but according to our law you have to make some statement. If it turns out to be true, we'll eat you. If it turns out to be false, our lion will eat you."
What should I say to Robinson to avoid being eaten?

📜 Leaflet #amazing_island

9 identical candies cost $11 with change, and 13 of the same candies cost $15 with pennies. How much does one candy cost up to one cent?

📜 Leaflet #scales

There are nuts in three boxes. The first one has 6 fewer nuts than the other two together, and the second one has 10 fewer nuts than the first and the third. How many nuts are there in the third box?

📜 Leaflet #scales

🎞 Mathematics and sex, Enjoy watching!

Smidge and Karlsson were each given the same pie. Karlsson started eating his pie one minute later than Smidge, and two minutes after that it turned out that Karlsson had already eaten as much as Smidge had left to eat. Prove that if Smidge and Karlsson had eaten the same pie together, they would have managed it in less than three minutes.

📜 Leaflet #scales

1) Are there two consecutive natural numbers such that the sum of the digits of each number is divisible by 4?
2) Are there two consecutive numbers with an equal sum of digits?

📜 Leaflet #yes_or_no

In all of the problems of the leaflet #yes_or_no, the answer is "Yes" or "No". If the answer is "Yes", give an example of when this might happen. If the answer is "No", you should explain why.

The monkey and the coconuts

Five men and a monkey were shipwrecked on an island. They spent the first day gathering coconuts. During the night, one man woke up and decided to take his share of the coconuts. He divided them into five piles. One coconut was left over so he gave it to the monkey, then hid his share, put the rest back together, and went back to sleep.

Soon a second man woke up and did the same thing. After dividing the coconuts into five piles, one coconut was left over which he gave to the monkey. He then hid his share, put the rest back together, and went back to bed. The third, fourth, and fifth man followed exactly the same procedure. The next morning, after they all woke up, they divided the remaining coconuts into five equal shares. This time no coconuts were left over.

How many coconuts were there in the original pile?

Can a month have a) 3; b) 4; c) 5; d) 6 Sundays?

📜 Leaflet #yes_or_no