The tasks of knights and liars are a kind of mathematical problems in which the characters appear:
- Liar ( rogue , vampire , madman , werewolf , ghoul ) - a person (or other creature), always telling a lie.
and his antagonist
- Knight ( man , righteous ), always telling the truth.
The solution to such problems usually comes down to enumerating options with the exception of those that lead to a contradiction.
There are tasks with three types of characters - knights, liars and normal people (option - spies). The latter can both lie and tell the truth (for example: the most difficult logical task ).
There are also whole classes of problems of the same type, but with other characters - problems about patients and doctors , problems about ghouls , collected in particular in the books of mathematician Raymond M. Sullian .
Content
Examples
Knights and liars live on the island. A traveler who met one of the locals asked him who he was. What will the resident answer?
The traveler went on the road connecting the city of liars and the city of knights. He wants to know which side each city is in. What question should he ask a passerby (not knowing whether he is a knight or a liar) in order to determine this?
Two people A and B, who are known to be either a knight, a liar, or a normal person, make the following statements:
A: B is a knight.
B: A is not a knight.
Prove that at least one of them is telling the truth, but he is not a knight.
On an island whose population is made up of only knights who always tell the truth, and liars who always lie, there is a research institute. Each of its employees once made two statements:
a) There are no ten people at the institute who work more than me.
b) At least one hundred people at the institute receive a salary greater than mine.
It is known that the load on all workers is different, as is the salary. How many people work in research institutes?
One of the variants of the problem of knights and liars is mentioned in the Spanish thriller " Trap of the Farm ." Also, a task of this type is found in the film " Labyrinth " by Jim Henson.
Notes
- Almost always, in these tasks, knights and liars can only say “yes” or “no” (options like “impossible to give an answer” or “don't know” are excluded), thus reporting one bit of information.
- The liar paradox is usually ignored in these tasks. In rare cases, it is indicated that "all those asked should be able to answer the question."
- In the vernacular, the knight is sometimes called the "righteous man."
- Also in such tasks can be present "tricks", they are also "jokers" "or ordinary people." Such characters can lie or tell the truth - at their discretion.
See also
- Logics
- Popularization of science