There are 100 statements.
1st one says: At least one statement is wrong.
2nd one says: At least two statements are wrong.
3rd one says: At least three statements are wrong.
4th one says: At least four statements are wrong.
...and so on till
100th one says: At least hundred statements are wrong.
Determine how many statements are actually wrong and how many are actually right?
Answer: Show answer
1st one says: At least one statement is wrong.
2nd one says: At least two statements are wrong.
3rd one says: At least three statements are wrong.
4th one says: At least four statements are wrong.
...and so on till
100th one says: At least hundred statements are wrong.
Determine how many statements are actually wrong and how many are actually right?
Answer: Show answer
Let's start looking at the statements one by one. The 100th statement is definitely wrong because it says at least all 100 are wrong. But if that was correct, then the 100th statement itself cannot be right!
=> 100th statement is wrong
=> 1st statement is correct
(so far 1 wrong and 1 correct)
Similarly, the 99th statement says that at least 99 statements are wrong, i.e. maximum 1 among 100 may be correct, which we have already concluded that the 1st one is correct. But in that case, the 99th statement itself cannot be correct, because if we say that 99th is correct then we will get total 2 correct statements (1st and 99th), which is conflicting with the 99th statement itself.
=> 99th statement is wrong
=> 2nd statement is correct
(so far 2 wrong and 2 correct)
Calculating in a similar fashion, we will finally get the last 50 statements to be wrong and the first 50 statements to be right.
=> 100th statement is wrong
=> 1st statement is correct
(so far 1 wrong and 1 correct)
Similarly, the 99th statement says that at least 99 statements are wrong, i.e. maximum 1 among 100 may be correct, which we have already concluded that the 1st one is correct. But in that case, the 99th statement itself cannot be correct, because if we say that 99th is correct then we will get total 2 correct statements (1st and 99th), which is conflicting with the 99th statement itself.
=> 99th statement is wrong
=> 2nd statement is correct
(so far 2 wrong and 2 correct)
Calculating in a similar fashion, we will finally get the last 50 statements to be wrong and the first 50 statements to be right.
1 comments
Write commentsnot satisfied with the explanation, kindly let me know if you can share more input on the same. Your assistance will be highly appreciated.
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