# Task 2. (2 points)

Knights and liars played "Chinese whispers" according to the following rules: the first in the chain whispers a number to the second, the second to the third, and so on. The last person in the chain announces the number out loud. At the same time, a knight repeats the same number that was told to them, while a liar adds or subtracts one.

The first person (a liar) whispered the number 7 to their neighbor. The last person announced the number 3 out loud.

After that, the participants played this game again, but this time they passed the numbers to each other in reverse order. The last person whispered the number 5 to their neighbor, and the first person announced the number 2 at the end of the game.

Who was the last person in the chain?
Answer: Knight

## Solution:

In the first game, the number does not change parity, which means that the number of liars in the chain from the 2nd to the last is even.

From the result of the second game, we get that the number of liars in the chain from the second-to-last to the first is odd.

This means that the first and last people are of different types, that is, the last one is a knight.