Task 2 - 290712

Thomas, Uwe, and Volker took the first three places in a mathematics olympiad, each of them a different place from the other two. The following three statements were made about this ranking:

(1) Thomas did not come in first.

(2) Uwe did not come in second.

(3) Volker came in second.

Of these three statements (1), (2), (3), exactly one is true.

Determine whether it is possible to determine from this which of the three students took first, second, and third place! If this is the case, give the ranking!
If (3) were the true statement, then it would follow, since (3) is true and (2) is false, that both Volker and Uwe would have taken second place; in contradiction to the problem text.

If (2) were the true statement, then it would follow, since (2) is true and (1), (3) are false, that none of the three students would have taken second place; also in contradiction to the problem text.

Thus, only (1) can be true. Since (2) is therefore false, it follows: Uwe came in second. From this and since (1) is true, it follows: Thomas came in third, Volker came in first.

This also shows that this ranking can be determined from the conditions of the problem text.