# How many statements on the list are in fact false?

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You find a forgotten list on an ancient piece of paper while cleaning your professor's office. It has the following written down:

Exactly 1 statement on this list is false.
Exactly 2 statements on this list are false.
Exactly 3 statements on this list are false.
Exactly 4 statements on this list are false.

How many statements on the list are in fact false?

posted Jul 22, 2017

exactly three statements are false because this statement/comment has to be true

Similar Puzzles

Two of the following statements are true and the other one is false:

1. This statement is true.
2. The first statement is false.
3. The second statement is true.

Which statement is false?

Exactly one of these numbered statements is true:
1. One of these statements is false.
2. Two of these statements are false.
3. Three of these statements are false.
4. Four of these statements are false.
5. Five of these statements are false.

Which of the statements is true?

Billy "The Knife," the infamous tough guy, was found murdered one night in an alleyway behind the nightclub he used to frequently visit. The police brought in three suspects on the next morning. One of the officers interrogated the three men and noted down the following statements.

Alex:
1. I did not kill Billy.
2. Jimmy is not my friend.
3. I knew Billy.

Jimmy:
1. I did not kill Billy.
2. Alex and Dexter are friends of mine.
3. Alex did not kill Billy.

Dexter:
1. I did not kill Billy.
2. Alex lied when he said that Jimmy was not his friend.
3. I do not know who killed Billy.

Only one of the three is guilty, and only one of each man statements is false. Who killed Billy the Knife ?

Xeno, Yves, and Zahara are best friends celebrating one of their own birthdays. They make the following statements:

Xeno says, "It's Yves' birthday!"
Yves says, "It's not Xeno's birthday!"
Zahara whispers, "It's __'s birthday", but so quietly that you can't make out which of the three names she said.

If I told you how many true statements were made, then you still wouldn't know whose birthday it is. Now that you know that, if I told you what Zahara said then you'd know whose birthday it is.

Whose birthday is it?