Problems

One person says: “I’m a liar.” Is he a native of the island of knights and liars?

In the language of the Ancient Tribe, the alphabet consists of only two letters: M and O. Two words are synonyms, if one can be obtained by from the other by a) the deletion of the letters MO or OOMM, b) adding in any place the letter combination of OM. Are the words OMM and MOO synonyms in the language of the Ancient Tribe?

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?

15 points are placed inside a \(4 \times 4\) square. Prove that it is possible to cut a unit square out of the \(4 \times 4\) square that does not contain any points.

On an island, there are knights who always tell the truth, and liars who always lie. What question would you need to ask the islander to find out if he has a crocodile at home?

An investigation is being conducted into the case of a stolen mustang. There are three suspects – Bill, Joe and Sam. At the trial, Sam said that the mustang was stolen by Joe. Bill and Joe also testified, but what they said, no one remembered, and all the records were lost. In the course of the trial it became clear that only one of the defendants had stolen the Mustang, and that only he had given a truthful testimony. So who stole the mustang?

True or false? Prince Charming went to find Cinderella. He reached the crossroads and started to daydream. Suddenly he sees the Big Bad Wolf. And everyone knows that this Big Bad Wolf on one day answers every question truthfully, and a day later he lies, he proceeds in such a manner on alternate days. Prince Charming can ask the Big Bad Wolf exactly one question, after which it is necessary for him to choose which of the two roads to go on. What question can Prince Charming ask the Big Bad Wolf to find out for sure which of the roads leads to the Magic kingdom?

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?

Five oaks are planted along two linear park alleys in such a way that there are three oaks along each alley, see picture. Where should we plant the sixth oak so that it will be possible to lay two more linear alleys, along each of which there would also be three oak trees growing?

Decipher the following puzzle. All the numbers indicated by the letter E, are even (not necessarily equal); all the numbers indicated by the letter O are odd (also not necessarily equal).