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?

Submitted by Dustin

Rating: 4.6667 (3 votes)

Solution: (Hide)

Short answer: Jer
Long answer: First, you can determine the veracity of A, B, D, and F to be false. C and E could be true and false, or false and true.
A - FALSE - Math Man
B - FALSE - Ady TZION
C - ??? - K Sengupta
D - FALSE - Jer
E - ??? - Bractals
F - FALSE - Larry
This leads us to the following arrangement for the speakers for part two. Also, we can determine the truth of certain of these statements, since H and J must be both true or both false, and they cannot be both true, they must be both false.
G - FALSE - Math Man
H - FALSE - Ady TZIDON
I - TRUE - K Sengupta or Jer?
J - FALSE - Jer or Bractals?
K - FALSE - Larry
We can assume O is false since M is true, and only one statement can be true.
L - FALSE - Math Man
M - TRUE - Ady TZIDON
N - FALSE - Jer or Bractals?
O - FALSE - Larry
This part is more difficult. "If X, then Y" is false only when X is true and Y is false. In other words, if Y is true, the whole statement is true. Since "then I am Larry" is true, statement R must be true. Since only one of the three is true, then P and Q must be false.
P - FALSE - Math Man
Q - FALSE - Jer or Bractals?
R - TRUE - Larry
Which leads us to the final status:
S - TRUE - Math Man
T - ??? - Jer or Bractals
So, since statement S is true, statement T must be false. Which means speaker T is, in fact, NOT Bractals, which means it must be Jer. Therefore, we know T, Q, N, and J are FALSE, and were stated by Jer. This means Bractals must have told the truth in statement E, so Jer could take position J.
Final Solution:
Jer is the consistent liar.
Fun facts:
K Sengupta is NOT a professional theremin player.
Jer's favourite colour is NOT green.
Larry does NOT own a grand piano.

Comments: ( You must be logged in to post comments.)

Subject	Author	Date
Solution	Math Man	2012-01-29 14:19:46
solution	Justin	2012-01-29 11:49:00

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