The murder mystery!!

@simplycoder-NsBEdD • Oct 17, 2024

Oct 17, 2024

799

Five friends Ramesh,Sudha,Mohan,Mona and Suresh planned to go on a vaccation.
Ramesh booked the tickets to travel and Suresh booked the hotel.

All of them were in the same compartment of the train.
The train passed through a tunnel and when it emerged out, it was found that Suresh was murdered.

Sudha called CID and separate interrogations took place and this is what they had to say.

Ramesh: I am innocent and Sudha was talking to Suresh when train was passing through tunnel.
Sudha:I am innocent and I wasnt talking to Suresh when train was passing through tunnel.
Mohan:I am innocent, Mona comitted the murder.
Mona:I am innocent one of the men commited the murder.

Upon the polygraphic tests results, it was revealed who murdered Suresh along with the truth in the statments made. Unfortunately, those papers were stolen and now CID team knows that there were only 4 true statements made and only one person comitted the murder.

Can you solve this mystery and help CID find the killer?

PS: This puzzle is reframed by me, however, I referred to the example given Dr.Kamla in lecture 2 of propositional logic. Please donot spoil the fun for others by posting solution after referring her explanation.

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born_star16

@born-star16-U2z3az • Jan 9, 2012

There were only 4 statements made and CID says there were only 4 true statements. So, everyone is innocent then.
Confusion......Confusion.........Confusion😲

I am sure I am not the killer.😛
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simplycoder

@simplycoder-NsBEdD • Jan 10, 2012

born_star16
There were only 4 statements made and CID says there were only 4 true statements. So, everyone is innocent then.
Confusion......Confusion.........Confusion😲

I am sure I am not the killer.😛
Each one of them makes 2 statements.
for example, statement made by Ramesh :I am innocent and Sudha was talking to Suresh when train was passing through tunnel. are two different statements clubbed into one compound statement.
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Dancer_Engineer

@dancer-engineer-EJ8rGI • Jan 10, 2012

Is it Sudha?

Following are the 4 true statements:
Ramesh: I am innocent and Sudha was talking to Suresh when train was passing through tunnel.
Mohan:I am innocent,
Mona:I am innocent

Following are the 4 false statements:
Sudha:I am innocent and I wasnt talking to Suresh when train was passing through tunnel.
Mohan: Mona comitted the murder.
Mona: one of the men commited the murder.
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simplycoder

@simplycoder-NsBEdD • Jan 10, 2012

Dancer_Engineer
Is it Sudha?

Following are the 4 true statements:
Ramesh: I am innocent and Sudha was talking to Suresh when train was passing through tunnel.
Mohan:I am innocent,
Mona:I am innocent

Following are the 4 false statements:
Sudha:I am innocent and I wasnt talking to Suresh when train was passing through tunnel.
Mohan: Mona comitted the murder.
Mona: one of the men commited the murder.
Yep you are correct...
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Dancer_Engineer

@dancer-engineer-EJ8rGI • Jan 10, 2012

simplycoder
Yep you are correct...
Quackarunne 😎
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PraveenKumar Purushothaman

@praveenkumar-66Ze92 • Jan 10, 2012

Whats the explanation???
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Dancer_Engineer

@dancer-engineer-EJ8rGI • Jan 10, 2012

Ok, I had roughly solved it on paper.

2minutes, I'll solve it freshly for you 😛
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Dancer_Engineer

@dancer-engineer-EJ8rGI • Jan 10, 2012

Ok, so the image has come bad and so has my handwriting. 😁

This is my approach to the puzzle:

1a, 1b are the two sentences which make one compound statement (1) as stated by SC.

With the statements given I have filled the table.
I see there are 3 statements in connection to Sudha, so I treated Sudha to be the murderer. So statement 2a, 2b are false.
So Sudha becomes the murderer, so all the others are innocent; so statement 1a, 3a, 4a are true.
Since Sudha is murderer, statement 1b against Sudha is true.
And since Sudha is the murderer, Mona commited the murder (3b) is false.
Since Sudha is the murderer, 'one of the men commited the murder' (4b) is also false.

Hence proved! 😎

PS: @SC, is this approach right? Took me 2-3 minutes, only after you made it clear that there are 8 statements. 😛
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simplycoder

@simplycoder-NsBEdD • Jan 10, 2012

The typical approach would be something like this.
Since it is given that only 4 statements are true and there is only one killer, it can be said that 3 people are innocent and one is guilty, this can be treated as 3 statements ('I am innocent') of 4 made are true and one is false.

This leaves us to the fact that the rest false statement is from the other group of statements. So in the other group, there are 3 false statements and only one true statement.

Now see the second statement made by Ramesh, he says that sudha was talking to suresh when the train was passing through the tunnel. This is contradicted by Sudha. Assuming Ramesh lied, sudha must be telling the truth or by assuming sudha lied, ramesh must be telling the truth. In both cases, we get 1 true statement which is the only true statement made from the second group of statements.

Now that we have found that either ramesh or sudha is telling the truth, we can say that mohan and mona are lying in second statement.

Mohan's second statement was "Mona comitted the murder" this is false and Mona's statement is
"One of the men comitted the murder", this is also false.

By Mohan's and Mona's second statement being false, it can be said that Both men didnot commit the murder and Mona also didnot commit the murder.From this, we get three true values in first group of statements, stating that Ramesh,Mona,Mohan were innocent. Since there has to be one false value, it has to be Sudha's first statement.

So Sudha commited the murder.
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PraveenKumar Purushothaman

@praveenkumar-66Ze92 • Jan 11, 2012

Awesome! 😀
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zaveri

@zaveri-5TD6Sk • May 18, 2012

superb ! you solved the case, the engineering way. I wonder if we engineers can make good investigators.
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