In downtown Gaussville, there are three buildings with different heights: The Euclid (E), The Newton (N) and The Galileo (G). Only one of the statements below is true.
 1. The Newton is not the shortest.
 2. The Euclid is the tallest.
 3. The Galileo is not the tallest.

Ordered from shortest to tallest in height, the buildings are
(A) N, G, E
(B) G, E, N
(C) E, N, G
(D) N, E, G
(E) E, G, N
Since only one of the given statements is true, then the other two statements are both false.

Assume that the second statement is true (then the other two are false).

If the second statement is true, then The Euclid is the tallest building.

Since the third statement is false, then The Galileo is the tallest building.

However, The Euclid and The Galileo cannot both be the tallest building so we have a contradiction. Therefore the second statement cannot be true.

Assume that the third statement is true.

Then The Galileo is not the tallest building.

Since the second statement must be false, then The Euclid is not the tallest building.

If both The Galileo and The Euclid are not the tallest building, then The Newton must be the tallest.

However, since the first statement must also be false, then The Newton is the shortest building and we have again reached a contradiction. Therefore, the third statement cannot be true.

Since both the second and third statements cannot be true, then the first statement must be true.

Since the first statement is true, then The Newton is either the second tallest building or the tallest building.

Since the third statement is false, then The Galileo is the tallest building which means that The Newton is the second tallest.

Since the second statement is false, then The Euclid is not the tallest and therefore must be the shortest (since The Newton is second tallest).

Ordered from shortest to tallest, the buildings are The Euclid (E), The Newton (N), and The Galileo (G).