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Which statements are true?

+1 vote
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Which statements are true?

  1. The number of the first true statement here added to the number of the second
    false statement gives the number of a statement which is true.

  2. There are more true statements than false.

  3. The number of the second true statement added to the number of the first false
    statement gives the number of a statement that is true.

  4. There are no two consecutive true statements.

  5. There are at most three false statements.

  6. If this puzzle consisted of statements 1 to 5 only, then the answer to the following
    question would still be the same.

posted Dec 24, 2014 by Bhavish D A

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There are 100 doors in a row, all doors are initially closed. A person walks through all doors multiple times and toggle (if open then close, if close then open) them in following way:

In first walk, the person toggles every door.

In second walk, the person toggles every second door, i.e., 2nd, 4th, 6th, 8th, …

In third walk, the person toggles every third door, i.e. 3rd, 6th, 9th, …

………
……….

In 100th walk, the person toggles 100th door.

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Which Of These Statements Is True?

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There are a hundred statements.

First person says: At least one of the statements is false.

Second person says: At least two of the statements is false.

Third person says: At least three of the statements are false.

Fourth person says: At least four of the statements are false.

..

..

..

Hundredth person says: At least a hundred of the statements are false.

Analysing it, how many statements do you think are false and how many are true?

...