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?

From the first step, Math Man, Ady TZIDON, Jer, and Larry are either all telling the truth, or all telling a lie. As only one person can be telling the truth, they must all be lying. That leaves either K Sengupta or Bractals as the truth teller, and the names to proceed are as follows:

Math Man
Ady Tzidon
K Sengupta/Jer
Jer/Bractals
Larry

Obviously Math Man is lying, as we know Jer did not tell the truth in the first grid. If Ady TZIDON is telling the truth, then K Sengupta/Jer is lying, which means Jer/Bractals is also telling the truth, so Ady must be lying. Since Ady is lying, that means K Sengupta/Jer is telling the truth. As Larry was not in position E above, he is lying, and either I or J must be telling the truth. Now we have the following:

Math Man
Ady TZIDON
Jer/Bractals
Larry

Math Man is lying again, as his name contains an "M". Ady however is telling the truth as he was in position H above, not I. So we now have three spots left (albeit with 4 candidates).

MathMan
Jer/Bractals
Larry

Math Man must be lying once more, as Larry is in position R, which would make both P and Q truthful. As statement P is a lie, Larry is telling the truth.

Math Man says "I am Math Man" which is true, meaning that:

Jer/Bractals stated "I am Bractals". As only one can be telling the truth, it can't be Bractals in position T.

Therefore, the consistent liar must be Jer.

Posted by Justin on 2012-01-29 11:49:00