Clever you!, Got a clue?

Logic Level 3

Gunda and Badmaash were the two notorious convicts, who were now arrested, and the police called you for a brief interrogation with them.

It is known that both of them tell the truth and lie on alternate days. On a particular day, if one of them tells the truth, then the other one lies.For an explicit example, if Gunda lies today, then Badmaash tells the truth. And tomorrow Gunda will tell the truth and Badmaash will lie. They both are known to this fact. and they both are in the same interrogation room.

Here is the interrogation done by $You$ :

$You$ asked $Gunda$ , "Will you tell the truth today?"

$Gunda$ replied, "Yes, I Will."

$You$ asked $Badmaash$ , "Is Gunda lying?"

$Badmaash$ replied, "Yes, he is lying."

$You$ asked $Gunda$ again, "If this whole interrogation ( $as$ $stated$ $above$ ) was done $yesterday$ and then If I had asked you that, "if $Badmaash$ was telling the truth?", what could possibly be your reply?"

$Gunda$ replied, "then I would have replied a NO."

It can be concluded from the above statement that:

Can you catch some liars for me. Here are some of them who make statements worth deceiving

Badmaash was telling the truth on interrogation day Cannot be determined. Gunda was telling the truth on interrogation day Badmaash was lying on the interrogation day It is an impossible scenario. Gunda was lying on interrogation day

1 solution

Ashish Menon
Apr 30, 2016

Abhay, great question of "gunda" and "badmaash" ;)

The answer is that Gunda was telling the truth that day. Suppose Gunda was lying, then he would have replied affirmatively for the first question but then Badmaash should have replied negatively to the second question. But then for the third question, again Gunda should have told the truth yesterday so he should have replied Yes, Badmaash lies yesterday which he didnt. So, since first and third statements are satisfactory, but the second violates the conditions, Gunda must not be lying that day.

Now, lets check the truthness. If Gunda was telling the truth that day, he should reply affirmatively, which he did. Then Badmaash who wpuld be lying should reply negatively which he did. Then for the third statement gunda should have lied yesterday. Since Badmaash lies today, he would have spoke truth yesterday. So yesterday's liar Gunda would reply No,Badmaash is lying, which he did confess today when he spoke the truth.

So, since this possibilty satisfies all the conditions of the question, Gunda was telling the truth on the day of interrogation.

Yes, this is the exact and right approach for the Question. Thanks a lot for your solution. :)

Abhay Tiwari - 5 years, 1 month ago

My pleasure.