Under a certain legal system, prisoners are allowed to make one statement. If their statement turns out to be true then they are hanged. If the statement turns out to be false then they are shot. One prisoner made a statement and the judge had no option but to set him free. Which one of the following could be that statement?

The correct option is "I will be shot".

To understand why this statement forces the judge to set the prisoner free, we can analyze the two possible scenarios defined by the legal system's rules:
1. If the statement is true, the prisoner must be hanged.
2. If the statement is false, the prisoner must be shot.

Let's evaluate the consequences of the statement "I will be shot" under both scenarios:

Scenario 1: Assume the statement is true.
If the statement is true, the rules dictate that the prisoner must be hanged. However, if the prisoner is hanged, his statement (that he would be shot) becomes false. This creates a logical contradiction because a true statement has resulted in an action that makes the statement false.

Scenario 2: Assume the statement is false.
If the statement is false, the rules dictate that the prisoner must be shot. However, if the prisoner is shot, his statement (that he would be shot) becomes true. This also creates a logical contradiction because a false statement has resulted in an action that makes the statement true.

Since both executing the prisoner by hanging (assuming truth) and executing him by shooting (assuming falsehood) lead to a logical contradiction, the judge cannot apply either rule without violating the legal system. Thus, to avoid a logical paradox, the judge has no option but to set the prisoner free.