perplexus.info :: Logic : Once a Liar, Always a Liar 2

Once a Liar, Always a Liar 2 (Posted on 2012-01-29)

Look at the 6 statements below (in the column at right is the name of the person who made each statement):

 A |   Jer is telling the truth.               |  Math Man
 B |   Math Man is telling the truth.          |  Ady TZIDON
 C |   I am a professional theremin player.    |  K Sengupta
 D |   Larry is telling the truth.             |  Jer
 E |   K Sengupta is lying.                    |  Bractals
 F |   Ady TZIDON is telling the truth.        |  Larry

Only 1 of the 6 people is telling the truth. Remove the name of the truth-teller and place the names of the remaining 5 in the same order in the next board, (for example, if Ady TZIDON is telling the truth, Ady TZIDON will be removed and in the next board you will place the names Math Man (in line G), K Sengupta (in line H), Jer (in line I), Bractals (in line J), and Larry (in line K) in the column at right.

 G |   Jer told the truth in the grid above.   |
 H |   The person in position I is lying.      |
 I |   The person in position J is lying.      |
 J |   My favourite colour is green.           |
 K |   I was in position E above.              |

Only 1 of the 5 people is telling the truth. Remove the truth-teller from the line-up and proceed as above with the 4 remaining names.

 L |   My name does not contain the letter 'M'.|
 M |   I was not in position I above.          |
 N |   The person in position M is lying.      |
 O |   I own a grand piano.                    |

Only 1 of the 4 people is telling the truth. Remove the truth-teller from the line-up and proceed as above with the 3 remaining names.

P| If Larry is in position R, then statement Q is truthful. |
Q| If Math Man is in position P, then statement R is a lie. |
R| If statement P is a lie, then I am Larry.                |

Only 1 of the 3 people is telling the truth. Remove the truth-teller from the line-up and proceeed as above with the 2 remaining names.

 S |   I am Math Man.                          |
 T |   I am Bractals.                          |

Only 1 of the 2 people is telling the truth. Remove the truth-teller from the line-up.

Who is the consistent liar?

See The Solution Submitted by Dustin

Rating: 4.6667 (3 votes)

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Solution

Comment 2 of 2 |

Suppose Math Man is telling the truth. Then, Jer is telling the truth, too. However, only one person is telling the truth. Therefore, Math Man is lying. That means that Jer is also lying. Jer said that Larry is telling the truth, so Larry is lying. Larry said that Ady TZIDON is telling the truth, so Ady TZIDON is lying. Therefore, either K Sengupta or Bractals is the truth-teller. If K Sengupta is a professional theremin player, then it is K Sengupta. If K Sengupta is not a professional theremin player, then it is Bractals.

Case 1:K Sengupta is a professional theremin player. Then, we remove K Sengupta. Here is the order.

G:Math Man

H:Ady TZIDON

I:Jer

J:Bractals

K:Larry

Math Man is lying because Jer lied. Larry is lying because he was in position F. If Ady TZIDON is telling the truth, then Jer is lying, so Bractals is telling the truth. However, there is only one truth-teller, so Ady TZIDON is lying and Jer is the truth-teller. Also, Bractals is lying, so Bractals's favorite color is not green. We remove Jer.

L:Math Man

M:Ady TZIDON

N:Bractals

O:Larry

Math Man's name does contain M, so he is lying. Ady TZIDON was in position H above, so Ady TZIDON is the truth-teller. Therefore, Bractals is lying. Also, Larry is lying, so he does not own a grand piano. We remove Ady TZIDON.

P:Math Man

Q:Bractals

R:Larry

P says that Q is true since Larry is in position R. Q says that R is false since Math Man is in position P. If P is true, then Q is true. However, there is only one true statement, so P is false. Therefore, Q is false, so R is true. We remove Larry.

S:Math Man

T:Bractals

Now, both statements are true. This is a contradiction, so K Sengupta is not a professional theremin player.

Case 2:K Sengupta is not a professional theremin player. Then, we remove Bractals. Here is the order.

G:Math Man

H:Ady TZIDON

I:K Sengupta

J:Jer

K:Larry

For the same reasons as Case 1, I is the true statement. We remove K Sengupta.

L:Math Man

M:Ady TZIDON

N:Jer

O:Larry

For the same reason as Case 1, Ady TZIDON is the truth-teller. We remove Ady TZIDON.

P:Math Man

Q:Jer

R:Larry

For the same reasons as Case 1, R is true. We remove Larry.

S:Math Man

T:Jer

Math Man is telling the truth, so Jer is the consistent liar.

Posted by Math Man on 2012-01-29 14:19:46

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