Distinguishing False Statements

We can't have $0$ false statements in the list since they all contradict each other, and thus at least two must be false. For this reason we also can't have $1$ false statement.

We can't have three false statements for that would make statement 3.) correct, in which case we could only have a maximum of two false statements.

If we have two false statements, then statement 2.) is correct and indeed statement 1.) and statement 3.) are then false, so we have achieved a consistent result. Thus the only conclusion is that there are $\boxed{2}$ false statements.

• Statement 3: "There are 3 false statements in this list." cannot be true because if it is true then it contracts itself. Therefore there are at least one statement is false in the list.
• Statement 1: "There are 1 false statement in this list." cannot be true, because if it is true then the false statement must be statement 3. Then statement 2 is true, which means that the other 2 statements including statement 1 are false.
• Statement 2: "There are 2 false statements in this list." must be true.

First, at most one of these 3 statements is correct, because they are exclusive of each other.

Second, there can't be all 3 wrong statements, because this implies the third statement is true and contradiction happens.

Therefore, there is only one true statement (and the other two are false). The answer is 2. (We must check the answer again then. If it's false, so the problem is illogic at the first place)

If 1 is correct, then there is one false statement, which would be 3, there would also be a second true statement (2), which contradicts #1 (or the other way around).

If three is correct, then all of them are incorrect, including three, so there can't be three false statements.

If two is correct, then 1 and 3 are incorrect, meaning that there is nothing to contradict 2, and two doesn't contradict itself, which means the answer is 2.

If 2nd statement is true then 1st and 3rd statements are false. So there are 2 false statements....

there cant be 3 false statements since the statement stating it has to be false then.but if we consider 2 false statements,then its probable because it may be the only true one while others are false.

We can't have 0 statements because they all gave different answers. So only 1 is telling the truth (2), and the other 2 is not (1 and 3). So the answer is 2.

There are only 3 statements and only 1 can be true. If the first one's true, then the other 2 are false, which is not what the statement says. If statement three's true, then all of them are false, which also contradicts the statement. Hence, statement 2 is true because then statement 1 and 3 would be false.

Answer = 2 are false according to statement 2

Clearly, the statements cannot all be true, as they are all contradictory. But it is impossible that only one is true, since whichever one it is would automatically make the other two false. Similarly, they cannot all be false, as that would make statement 3 true, which is also contradictory. Thus there are two false statements; they are 1 and 3, and statement 2 is indeed true.

1. There is only 1 false statement in this list. => There is no false statements in this statement.
2. There are only 2 false statements in this list. => There is one false statements in this statement.
3. There are only 3 false statements in this list. => There is one false statements in this statement.

so totally two false statements are there in the lists