\section*{Task 5 - 041215}

In an IL 18 of Interflug, which flies to Berlin, five passengers are sitting next to each other in a row. Their professions are: Journalist, Precision Mechanic, Teacher, Captain, and Engineer. They belong to the following nationalities: Poland, GDR, Hungary, Cyprus, and USSR. They are of different ages (21, 24, 32, 40, and 52 years). The passengers engage in different sports (Handball, Swimming, Volleyball, Athletics, and Football). Their travel destinations are: Berlin, Leipzig, Dresden, Karl-Marx-City, and Rostock.

From conversations, we gather the following information:

(1) The Engineer is sitting all the way to the left.

(2) The Volleyball player has the middle seat.

(3) The Pole is a Journalist.

(4) The Precision Mechanic is 21 years old.

(5) The Teacher practices swimming.

(6) The Captain is traveling to Rostock.

(7) The Handball player is from the GDR.

(8) The traveler from the Soviet Union is flying to Leipzig.

(9) The traveler to Berlin is 32 years old.

(10) The Athlete has Karl-Marx-City as their travel destination.

(11) The traveler from the GDR is sitting next to the traveler from Hungary.

(12) The 52-year-old is sitting next to the traveler heading to Dresden.

(13) The 24-year-old is sitting next to the traveler heading to Leipzig.

(14) The Engineer is sitting next to the Cypriot.

a) How old is the Captain?

b) What nationality does the Football player have?

Show that the information provided is sufficient to answer both questions uniquely!
}

The seats are numbered from left to right as 1, 2, 3, 4, and 5.

Claim:

(1) The engineer sits on seat 1.

(15) The Cypriot sits on seat 2 because of (1) and (14).

(16) The traveler from the USSR sits on seat 1, he is an engineer, flies to Leipzig, and is a football player.

Proof: The traveler from Poland does not sit on seat 1 because of (1) and (3), not the traveler from East Germany and the one from Hungary because of (11) and (15), and not the traveler from Cyprus because of (15). Because of (8), he flies to Leipzig and because of (10), he is not an athlete, because of (1) and (5) not a swimmer, because of (7) not a handball player, and because of (2) not a volleyball player. Thus, the answer to a) is: The football player is a citizen of the USSR.

Claim:

(17) The Cypriot is 24 years old because of (13), (16), and (14).

(18) The captain plays volleyball or handball.

Proof: The captain does not play football because of (16). He is not an athlete because of (6) and (10) and not a swimmer because of (5).

Claim:

(19) The captain is Hungarian or German.

Proof: The captain is not from the USSR because of (16), not from Poland because of (3), and not from Cyprus because of (18), (2), and (15) or (18) and (7).

Claim:

(20) The captain sits on seat 3, 4, or 5 because of (1), (15), and (19).

(21) The captain is 40 or 52 years old.

Proof: He is not 21 years old because of (4), not 24 years old because of (17) and (19), and not 32 years old because of (6) and (9).

Claim:

(22) The Cypriot on seat 2 is traveling to Dresden.

Proof: He is not traveling to Berlin because of (9) and (17), not to Rostock because of (19) and (6), not to Leipzig because of (16), and not to Karl-Marx-Stadt, because then he would be an athlete because of (10), thus not the captain because of (18), not a teacher because of (5), not a journalist because of (3), but a precision mechanic. Then he would be 21 years old because of (4), which contradicts (17).

Claim:

(23) The captain is 40 years old.

Proof: Suppose this were not the case, then he would be 52 years old because of (21) and would sit on seat 3 because of (12), (22), and (16). He would thus be a volleyball player because of (2) and Hungarian because of (7) and (19). Then, because of (11) and (15), the German would sit on seat 4, not an engineer because of (16), not a teacher because of (7) and (5), not a journalist because of (3), but a precision mechanic and therefore 21 years old because of (4). Thus, the traveler from East Germany would not have Berlin as a destination because of (9) and not the destinations Leipzig because of (16), Dresden because of (22), Rostock because of (6), and Karl-Marx-Stadt because of (7) and (10), which contradicts the assumption that one of the five cities is his destination. Thus, the answer to b) is: The captain is 40 years old.

Adapted from [2]

\subsection*{9.6.2 II. Round 1964, Class 12}