# Which statements are true?

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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
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+1 vote
1. (1/10) statement is false
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There are 13 caves arranged in a circle. There is a thief hiding in one of the caves. Each day the the thief can move to any one of of the caves that is adjacent to the cave in which he was staying the previous day. And each day, you are allowed to enter any two caves of your choice.

What is the minimum number of days to guarantee in which you can catch the thief?

Note: Thief may or may not move to adjacent cave. You can check any two caves, not necessarily be adjacent. If thief and you exchange your caves, you will surely cross at some point, and you can catch the thief immediately.

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.

Which doors are open in the end?

There are hundred statements which go as follows;

Statement 1: At least one of these statements is false.

Statement 2: At least two of these statements are false.

Statement 3: At least three of these statements are false.

Statement 4: At least four of these statements are false.

Statement 100: At least a hundred of these statements are false.

What is the maximum number of statements that can be true?