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## Question

From logic puzzle book:

When a psychiatrist was found murdered in his apartment, four of his patients were questioned about his death.

I. The police knew from the testimony of witnesses that each of the four patients had been alone with the psychiatrist in his apartment just once on the day of his death.

II. Before the four patients were questioned, they met and agreed that every statement each of them would make to the police would be a lie.

Each patient made two statements, as follows:

Avery:

1. None of us four killed the psychiatrist.

2. The psychiatrist was alive when I left.

Blake:

3. I was the second to arrive.

4. The psychiatrist was dead when I arrived.

Crown:

5. I was the third to arrive.

6. The psychiatrist was alive when I left.

Davis:

7. The killer did not arrive after I did.

8. The psychiatrist was dead when I arrived.

Which one of the four patients killed the psychiatrist?

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...Avery?

Logic

First, since we know they are all lying, change the meaning of each statement as follows:

Avery:

1. One of us four killed the psychiatrist.

2. The psychiatrist was dead when I left.

Blake:

3. I was not second to arrive.

4. The psychiatrist was alive when I arrived.

Crown:

5. I was not third to arrive.

6. The psychiatrist was dead when I left.

Davis:

7. The killer arrived after I did.

8. The psychiatrist was alive when I arrived.

It makes sense that the first two to arrive are the two who saw him alive - Davis and Blake

Blake was not second, so he was first.

The killer arrived after Davis, so he was not the killer.

This leaves Avery and Crown... Crown wasn't third, so he was last.

The order is as follows:

Blake (alive when arrived)

Davis (alive when arrived)

Avery (dead when left)

Crown (dead when left)

Thus, Avery must have killed the psychiatrist.

Edited by Oboe Passion
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They arrived in the order Blake, Davis, Avery, and Crown, and Avery was the killer.

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...Avery?

Logic

First, since we know they are all lying, change the meaning of each statement as follows:

Avery:

1. One of us four killed the psychiatrist.

2. The psychiatrist was dead when I left.

Blake:

3. I was not second to arrive.

4. The psychiatrist was alive when I arrived.

Crown:

5. I was not third to arrive.

6. The psychiatrist was dead when I left.

Davis:

7. The killer arrived after I did.

8. The psychiatrist was alive when I arrived.

It makes sense that the first two to arrive are the two who saw him alive - Davis and Blake

Blake was not second, so he was first.

The killer arrived after Davis, so he was not the killer.

This leaves Avery and Crown... Crown wasn't third, so he was last.

The order is as follows:

Blake (alive when arrived)

Davis (alive when arrived)

Avery (dead when left)

Crown (dead when left)

Thus, Avery must have killed the psychiatrist.

They arrived in the order Blake, Davis, Avery, and Crown, and Avery was the killer.

Correct! Nice work!

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I agree with everything apart from it could have been Davis. His statement is that the psychiatrist was alive when he arrived (not neccesarily when he left). Similarly, Avery states that he was dead when he left. He could also have been dead when he arrived.

Correct! Nice work!

Edited by fabpig
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I just reread Davis's quote about the killer arriving after he did.

I agree with everything apart from it could have been Davis. His statement is that the psychiatrist was alive when he arrived (not neccesarily when he left). Similarly, Avery states that he was dead when he left. He could also have been dead when he arrived.

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that Davis did it. What if the 7th statement, when translated to truth, becomes "The killer did not arrive before I did." That leaves open the possibility that Davis could have been the killer (i.e., the killer arrived at the same time that Davis did).

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I am certain it was

Avery

..i saw him!.Kidding the facts show avery was the killer

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Patient: Arrival: Leaving: Number:

Avery.............................

Blake.............................

Crown.............................

Davis.............................

The elements of the arrival collumn represent the state of the doctor when the patient arrived, the ones in the leaving represent the state of the doctor when he left, and the number indicates the number of the patient in the arrival order.

From statements 2, 4, 6 and 8 we get the following:

Patient: Arrival: Leaving: Number:

Avery.............Dead............

Blake....Alive....................

Crown.............Dead............

Davis....Alive....................

This means that Blake and Davis arrived before Avery and Crown, so the possible order numbers of Blake and Davis are 1 and 2, and for Avery and Crown - 3 and 4.

Statements 3 and 5 help us with the order and we get:

Patient: Arrival: Leaving: Number:

Avery.............Dead.....3......

Blake....Alive....Alive....1......

Crown....Dead.....Dead.....4......

Davis....Alive.............2......

We exclude Blake and Crown as possible killers. After reading carefully statement 8 we get that the killer is:

Avery

I see the others getting the same result, so I see no reason for beeng wrong.

Edited by Ianis G. Vasilev

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