## Tuesday, May 31, 2011

### Usual Suspects

Four suspects; A, B, C and D have been arrested for possibly stealing the car of the chief of police. They were all interviewed personally by the chief, and were hooked up to the lie detector.

Each suspect gave three statements during the examinations, that are listed below:
Suspect A:
In high-school I was in the same class as suspect C.
Suspect B has no driving license.
The thief didn't know that it was the car of the chief of police.

Suspect B:
Suspect C is the guilty one.
Suspect A is not guilty.
I never sat behind the wheel of a car.

Suspect C:
I never met suspect A until today.
Suspect B is innocent.
Suspect D is the guilty one.

Suspect D:
Suspect C is innocent.
I didn't do it.
Suspect A is the guilty one.

Unfortunately, there was a lightning strike and the machine went haywire. After the recovery process, the machine only reported that exactly four of the twelve statements were true, but not which ones. And now all four suspects have gotten lawyers and are refusing to be re-interviewed.

Can you figure out which suspect did it?

1. We first pair the comments into true/false pairs that must be opposite each other. Those pairs are: 1&7, 4&10, 5&12, 9&11. Since we know that there are exactly four true statements, and at least one of each of those pairs must be true, that means that the other four statements (2, 3, 6 & 8) are all false.
Statement 8 is: "Suspect B is innocent." We therefore know that since 8 must be false, suspect B must be guilty.

The way all the comments fall as true / false is as follows:
2 false
3 false
4 false
6 false
8 false
9 false
12 false

5 true
10 true
11 true

1&7 undeterminable, one of each.

2. Suspect A because how would he know that the thief didn't know that the car was the chief's?

3. suspect A

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