**Puzzle:** There are 100 statements.

1^{st} one says : at least one is wrong.

2^{nd} one says : at least two are wrong.

3^{rd} one says : at least three are wrong.

4^{th} one says : at least four are wrong.

and so on.

100^{th} one says : at least 100 are wrong.

How many statements are actually wrong and how many actually right ?

**Solution:**

100^{th} statement is definitely wrong because it says at least 100 are wrong.

But if that is correct, then 100 statement itself cannot be right.

=> 100^{th} statement is wrong and

=> 1^{st} statement is correct.

99^{th} statement cannot be correct because if it were correct,

then two statements would become correct (1^{st} and 99^{th} itself.)

But 99^{th} statement says that atleast 99 are wrong.

=> 99^{th} is wrong and

=> 2^{nd} is correct.

calculating so on…

50 statements are right (the first 50 ones)

remaining 50 statements are wrong.

errr…what is the statement?

Question not clear, Please share more details

Question not clear

Nice explanation…!!!

Question is that, in those 100 statements, not all are right. So they wanted to know how many are right and how many wrong.

Consider from 100th statement, which says at least 100 are wrong. That means, according to 100th statement, none of them are correct including itself, hence 100th statement cannot be correct at all. This conclusion clears the path for 1st statement, which tells us that, at least one is wrong, in this case we concluded that 100th one is definitely wrong.

Result: 100th is wrong, and 1st is correct, Total: 1 Correct, and 1 wrong

Moving to 99th statement, which says, at least 99 are wrong, means according to it 1 among 100 is correct, which we already concluded that 1st is correct based on above conclusion. If it is so, then 99th cannot be correct, because if we conclude 99th is correct, then we will get total of 2 correct so far, which is conflicting with 99th statement. Therefore, so far, 100 and 99th statements are not correct, which makes us conclude that 2nd is correct which says 2 are wrong (as we concluded 100 and 99).

If we continue like this, it will go on till 51st statement, where we will end up totalling 50 correct and 50 wrong statements.

Hope it clears.