truthful, liar and random

Logic Level 2

Tanha always tells the truth,

Faiza always lies,

Rafsan sometimes lies and sometimes tells truth,

Saad either lies all day or tells the truth all day.

You make a phone call to them. The 1st person says: I'm Tanha. The 2nd person takes the phone and says: That's true. The 3rd person says: No, that(1st person) was Rafsan.

As they are all kids you didn't recognize them. Then Saad takes the phone and says: The 1st one was Faiza. The 2nd one was Rafsan.

What is the serial of Tanha, Faiza and Rafsan?

1, 3, 2 2, 1, 3 3, 2, 1 3, 1, 2 2, 3, 1 1, 2, 3

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2 solutions

Saya Suka
Jan 19, 2021

Voice #1 : I'm Tanha.
Voice #2 : That's true.
Voice #3 : No, that (1st person) was Rafsan.
Saad : The 1st one was Faiza. The 2nd one was Rafsan.
First, remember that Saad is consistent for the whole day, so both his statements must have the same truth values (nowhere in the puzzle said anything about the call made a minute before midnight).
Second, note that voice #2 corroborated with #1, so their statements must have the same truth values, too. So, you can bet that Rafsan must be one of the first two, no matter whether it's by partnering with Tanha in his angelic mood or working with Faiza in his devilish one because Tanha and Faiza just don't mix well together considering their polar opposite personality.
Now, let's look at the statement by voice #3. It opposed not only the first 2 voices, but was also in contrast to what Saad said. Analyzing Saad's statements deeper, they match neither 1&2 grouped voices nor the lone voice #3. So we have a 3-sided triangle here, but we know that the opposition between 12 vs 3 is solid and the truth must lie within either of the kid(s) because of the existence of the two persons, one who always tells the truth and another who always lies. So, we can conclude that Saad's statements are both false; that Faiza can never be voice #1 nor Rafsan voice #2. But we already know that Rafsan was in the grouped voice, and by knowing that Saad was in his bad day that we cannot trust his statements at all, so Rafsan must be the 1st voice and lying by impersonating Tanha over the phone. His accomplice must be Faiza as voice #2 and Tanha as voice #3 told the truth about Rafsan doing the impersonation of him.
Conclusions :
Tanha = 3
Faiza = 2
Rafsan = 1

One truth trumps over a million lies.

Truth is absolute. You can build lies around one truth by changing just one little part of it one by one to get a different lie each time, because truth is like AND logic gate, just a measly 0 can ruin all of the 999 other 1s. Even so, it's also like a veto power; the truth can stand tall and alone against all the lies and deny them all.

Saya Suka - 4 months, 3 weeks ago
Saad Khondoker
Jan 19, 2021

The possible combinations are:

(1st person)(2nd person)(3rd person)-(correctness of 1st sentence)(correctness of 2nd sentence)(correctness of 3rd sentence)

[C-correct(if possible according to the statement); W-wrong(if impossible according to the statement)]

  1. TFR -- CWC

  2. TRF -- CCC

  3. RTF -- CWW

  4. RFT-- CCC

  5. FTR -- CWC

  6. FRT -- CCW

So we get the serial according to the sentences for case 2 and 4.

now, Saad says, "1st person was Faiza" which does not match with 2 or 4. So Saad is lying today. His second sentence is "2nd person was Rafsan." which must also be a lie. In case 2, 2nd person is Rafsan which is invalid now. So case 4 must be true.

So the position of Tanha, Faiza and Rafsan is 3rd, 2nd and 1st. (3, 2, 1)

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