Saturday, November 7, 2015

Solution to: Daring Thoughtless Thief Puzzle

A daring, rather thoughtless thief once stole a car of the police chief. The police immediately started an investigation and on the basis of witness depositions, four suspects were arrested that were seen near the car at the time of the crime. Because the chief of police took the case very seriously, he decided to examine the four suspects personally using a lie detector. Each suspect gave three statements during the examinations, as follows:
Suspect A:1. In high-school I was in the same class as suspect C.2. Suspect B has no driving license.3. The thief didn't know that it was the car of the chief of police.
Suspect B:1. Suspect C is the guilty one.2. Suspect A is not guilty.3. I never sat behind the wheel of a car.
Suspect C:1. I never met suspect A until today.2. Suspect B is innocent.3. Suspect D is the guilty one.
Suspect D:1. Suspect C is innocent.2. I didn't do it.3. Suspect A is the guilty one.
With so many contradicting statements, the chief of police lost track. To make things worse, it appeared that the lie-detector didn't quite work yet as it should, because the machine only reported that exactly four of the twelve statements were true, but not which ones.Now the big Question : Who is the thief??

Solution:
There are five statements in which nothing is said about the possible offender: A1, A2, A3, B3, and C1. The statements A1 and C1 seem to be completely contradictory, but that is not the case! Although at most one of these statements can be true, they can also be both false!For example, suspects A and C might only know each other from primary school. About the statements A2 and B3 not much can be said (although it seems unlikely that statement A2 would be false and at the same time statement B3 would be true). In addition, it follows from the introduction that statement A3 is true.On the basis of an assumption about which suspect is the offender, we can count how many of the remaining statements are true:
 Statement: A is the offender: B is the offender: C is the offender: D is the offender: None of the suspects is the offender: B1 false false true false false B2 false true true true true C2 true false true true true C3 false false false true false D1 true true false true true D2 true true true false true D3 true false false false false Total: 4 true, 3 false 3 true, 4 false 4 true, 3 false 4 true, 3 false 4 true, 3 false

Combined with the fact that statement A3 is true, this gives:
 A is the offender: B is the offender: C is the offender: D is the offender: None of the suspects is the offender: Total: 5 true, 3 false 4 true, 4 false 5 true, 3 false 5 true, 3 false 5 true, 3 false

Because it was given that exactly four statements were true, the statements A1, A2, B3, and C1 must be false, and suspect B must be the offender.