# Task № 4.1

## Condition:

On an island of knights, who always tell the truth, and liars, who always lie, a five-story building was built. One resident lived on each floor. One day, each of them made the same statement:

"There are more liars above me than knights below me!"

How many liars can live in this building?
# Answer: 3

## Exact match of the answer -1 point

## Solution.

Notice that the person living on the 5th floor is definitely lying, as there is no one living above them, including liars. Therefore, there are 0 liars above them, and 0 or more knights below. Now consider the resident on the 1st floor. They definitely told the truth, as there are 0 knights below them, and at least 1 liar living above, specifically the one on the 5th floor.

Now let's focus on the resident on the 4th floor. Above them lives exactly 1 liar, and below - at least 1 knight on the 1st floor. Therefore, their statement is false in any case. This means they are a liar. Then, the resident on the 2nd floor, similar to the reasoning about the one on the 1st floor, is a knight. The only one left to determine is the resident on the 3rd floor. Above them live 2 liars, and below - 2 knights. Therefore, their statement is false. Hence, they are a liar.

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