### Brain Teasers

# But I Need to Know X!

X statements below are true.

1. X is 3.

2. If X is 2, then the following statement is false.

3. If X is 2, then the previous statement is true.

4. X is less than 4.

5. X is a square number.

6. If X is less than 3, then the previous statement is false.

7. If X is greater than 2, then the previous statement is false.

Which statements are true?

1. X is 3.

2. If X is 2, then the following statement is false.

3. If X is 2, then the previous statement is true.

4. X is less than 4.

5. X is a square number.

6. If X is less than 3, then the previous statement is false.

7. If X is greater than 2, then the previous statement is false.

Which statements are true?

### Hint

All of the statements involve X in them, but some of the statements give direct information about whether they're true or not, and also potential hints for X.### Answer

If X is 2, then statements 2 and 3 create a paradox. Therefore, X is not 2, so statements 2 and 3 are both true because the "if" part is not satisfied.Therefore, statement 6 must be true, because if X is less than 3, we know X must be 2. In this case, statement 5 is false.

However, because statement 6 is true, there are at least 3 true statements, meaning we can't conclude if statement 5 is false based on this statement alone.

Statement 7 is false because X is definitely greater than 2, and the previous statement was true.

Statement 1 and 4 must be false, because their truth will imply their falseness.

For example, if statement 4 was true, then it won't be satisfied anymore (as there are at least 4 statements true), so it can't be true.

But statement 5 must then be true, else statements 1 and 4 will become true.

Conveniently, X is 4, and is a square number, as statement 5 implies.

Therefore, statements 2, 3, 5, 6 are true.

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