# 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

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 ?

In a carrom board game competition, m boys n girls (m > n > 1) of a school participate, in which every student has to play exactly one game with every other student.

Out of the total games played, it was found that in 221 games one player was a boy and the other player was a girl.

Consider the following statements:
I. The total number of students that participated in the competition is 30.
II. The number of games in which both players were girls is 78.

Which of the statements given above is/are correct?
(a) I only (b) II only
(c) Both I and II (d) Neither I nor II.

+1 vote
1. (1/10) statement is false
2. (2/10) statement is false
3. (3/10) statement is false
4. (4/10) statement is false
5. (5/10) statement is false
6. (6/10) statement is false
7. (7/10) statement is false
8. (8/10) statement is false
9. (9/10) statement is false
10. (10/10) statement is false.