Solution to: Thoughtless Thief
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 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:|
|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.