## Task 4 - 040924

Jutta, Günter, and Klaus are participating in the second stage of the Mathematics Olympiad.

(1) They work (not necessarily in this order) in rooms 48, 49, 50.

(2) Jutta and Günter are the same age, Klaus is one year older than Jutta.

(3) Their three mathematics teachers, Mr. Adler, Mr. Bär, and Mr. Drossel, supervise in these three rooms during the work, but none of them supervises in the room where their own student works.

(4) Mr. Bär has the same first name as his student.

(5) The number of the room where Mr. Drossel supervises corresponds to one and a half times his age.

(6) Günter's room has a higher number than Klaus's room.

(7) The three students together are exactly as old as the number of the room where Jutta works.

(8) Jutta does not know Mr. Drossel.

What is Mr. Bär's first name? In which room does he supervise? (In the age specification, only full years are considered.)
From the statements (1) to (8) it follows:

(9) Mr. Drossel supervises in Room 48. (due to (1) and (5))

(10) Jutta works in Room 49. (due to (1), (2), and (7))

(11) Günter works in Room 50, Klaus in 48. (due to (1), (10), and (6))

(12) Günter is a student of Mr. Drossel. (due to (8), (9), and (11))

(13) Klaus is a student of Mr. Bär. (due to (12) and (4))

(14) Jutta is a student of Mr. Adler. (due to (12) and (13))

(15) Mr. Adler supervises in Room 50. (due to (3), (9), (10), (14))

(16) Mr. Bär is named Klaus and supervises in Room 49. (due to (4), (13), and (9) and (15)).

Solutions of the 2nd Round 1964 adopted from [5]

### 6.6.3 3rd Round 1964, Class 9