Why don't you just tell me who is who?

Logic Level 3

In a small village there are 4 families. Interestingly, each family has a pair of twin sisters. Let the elder sisters be $ABCD$ and the younger sisters be $abcd$ . One day, you went to the village and saw 8 of them and asked, "Which family are each of you belong?"

$A$ says, " $B$ and $a$ are not twin sisters."

$B$ says, " $C$ and $d$ are twin sisters. "

$C$ says, " $D$ and $c$ are not twin sisters."

$D$ says, "Among $ABC$ , only the elder sister of $d$ is telling the truth."

Given that $D$ is telling the truth, can you know which two are a pair?

(A,d)

(B,b)

(C,a)

(D,c)

(A,a)

(B,b)

(C,c)

(D,d)

(A,b)

(B,d)

(C,c)

(D,a)

(A,c)

(B,a)

(C,d)

(D,b)

4 solutions

Antonius Henry Setiawan
Mar 26, 2014

There are 3 scenario based on D statement that only the elder sister of d telling the truth.

Scenario 1 (A is telling the truth) :

A says, B and c are not twin sister (truth)
B says, C and d are twin sister (lie). The truth is C and d are not twin sister
C says, D and c are not twin sister (lie). The truth is D and c are twin sister

Result of Scenario 1 : (A,d) (D,c)

Scenario 2 (B is telling the truth) :

A says, B and c are not twin sister (lie). The truth is B and c are twin sister
B says, C and d are twin sister (truth).
C says, D and c are not twin sister (lie). The truth is D and c are twin sister

Result of Scenario 2 : (B,d) (B,c) (C,d) (D,c)

Scenario 3 (C is telling the truth) :

A says, B and c are not twin sister (lie). The truth is B and c are twin sister
B says, C and d are twin sister (lie). The truth is C and d are not twin sister
C says, D and c are not twin sister (truth).

Result of Scenario 3 : (C,d) (B,c). This scenario is not possible because the truth from B statement is C and d are not twin sister

Based on the 3 scenario above, the only possible scenario is Scenario 1. So the answer must contains (A,d) and (D,c)

Prem Kumar
Mar 27, 2014

Condition: Only the elder sister of 'd' among A,B and C is telling the truth. B says that C is the elder sister of D. Therefor B can not be the elder sister of d, because if she is, then she has to speak truth, and she speaks that she is not the elder sister of 'd' ( and C is). Therefor, B is a liar, and hence, it is a lie that C is the elder sister of d. HENCE, C IS ALSO A LIAR ( because C is not the elder sister of d). Therefor, A is not a liar. Hence A is the elder sister of d. There is only one option with that option...!

Ka Kei Yeung
Apr 6, 2014

B: C and d are twin sisters. C were the elder sister of d then she would be the one telling the truth and thus B is lying. This is contradiction already. This means C is NOT the twin sister of d and she is also only lying. Then A is the only person telling the truth and is the elder sister of d. There is only one option with such pair in the answer.

Heru Fianisal
Apr 6, 2014

(1). Based on D statement, that the elder sister of d is among ABC and only she tells truth, we can rule out (D,d) or D isn't the elder sister of d.

(2). From each ABC statements, we may easily notice that B statement is kind of paradoxical: if B tells truth, then B should be the twin sister of d (1), while in the statement B states the twin sister of d is C. Thus, from B, we can rule out (B,d) and (C,d).

(3). From (1) and (2), we can get one truth: A is the elder sister of D.

In conclusion, the answer should not contains (B,d), (C,d) and (D,d); and must contains (A,d).

Why don't you just tell me who is who?

4 solutions

0 pending reports