5-4. Andrei, Boris, Vladimir, and Dmitry each made two statements. For each boy, one of his statements turned out to be true, and the other - false.

Andrei: "Boris is not the tallest among us four." "Vladimir is the shortest among us four."

Boris: "Andrei is the oldest in the room." "Andrei is the shortest in the room."

Vladimir: "Dmitry is taller than me." "Dmitry is older than me."

Dmitry: "Both of Vladimir's statements are true." "I am the oldest person in the room."

It is known that there are no two boys of the same height or age. What is the name of the tallest boy?
Answer: Vladimir.

Solution. The first statement of Dmitry is incorrect, as it contradicts the condition of the problem. Therefore, Dmitry is the oldest. Consequently, the first statement of Boris is incorrect, so Andrey is the shortest. From this, it follows that the second statement of Andrey is incorrect, so Boris is not the tallest. Also, the second statement of Vladimir is correct, so Dmitry is not taller than Vladimir. Then, the only one who can be the tallest is Vladimir.