## Task 5 - 040935

At a puzzle afternoon, the best young mathematician in the class is given the task of guessing a certain real number. His classmates take turns naming properties of this number:

Klaus: "The number is divisible by 4 without a remainder."

Inge: "The number is the radius of a circle whose circumference is 2."

Günter: "The number is less than 3."

Monika: "The number is the length of the diagonal of a square whose side has a length of 2."

Bärbel: "The number is irrational."

Peter: "The number is the area of an equilateral triangle whose side has a length of 2." Furthermore, he learns that of the students Klaus and Inge, Günter and Monika, and Bärbel and Peter, exactly one of each pair spoke the truth.

What is the number?
If Peter had told the truth, Bärbel's statement would have to be false, since exactly one of them is supposed to have told the truth.

This assumption leads to a contradiction, as Peter also characterized the number as irrational. Therefore, Bärbel told the truth.

Accordingly, Klaus's statement is false and Inge's statement is correct. From it follows: $x=\frac{1}{\pi}$

The statements of Günter and Monika are superfluous.