A pretty weird robbery
In a town there are 2 types of persons , either members of the family true either members of the family false. Remind that true members always tell the truth while false always lie. Last night the town's supermarket was robed. The police decided that there were 2 robbers and arrested 5 suspects ( A , B , C , D and E). All of them were interviewed and made 2 statements. Knowing the statements which are presented below find out who are the 2 robbers.
A. 1. At most one from B and E is guilty.
2. D is one of the robbers.
B. 1. A and C are both guilty.
2. E is not guilty.
C. 1. At least one from D and E is guilty.
2. It is unfair to suspect B.
D. 1. Exactly one from B and A is guilty.
2. C is the second robber.
E. 1. Neither C nor D are guilty. 2. A is surely one of the robbers.
Insert your answer using the values 2 and 1 in the order from A to E where 2 means robber and 1 means that the person isn't guilty. For example if A and B are guilty your answer should be 22111.
Try to deduce who is guilty based only on the explicit statements given by the problem.
You can assume that none of the suspects affirms he/she is not guilty unless he/she explicitly affirms so in their statements.
The answer is 11122.
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A : At most one from B and E is guilty. D is one of the robbers.
B : A and C are both guilty. E is not guilty.
C : At least one from D and E is guilty. It is unfair to suspect B.
D : Exactly one from B and A is guilty. C is the second robber.
E : Neither C nor D are guilty. A is surely one of the robbers.
10 statements were given, but not many of them left a finality feeling by their yet to be proven conclusions. But even though we didn't know whether they're telling the truths or not, we can definitely tell apart those who're on the same page or being contradictory with one another.
(D/0) + (AC/E) + (X/B) + (C/0) + (A/CD)
With this, we can see that B & D are both accusing C in unison while E defended C & D while accusing A. Also, A accused D and B accused A along with C as we mentioned earlier.
Because E's and B's statements are not consistent with each other, in which they both accused A but towards C, one took an offensive stance while the other being defensive of C. This situation would never, ever happened if both of them (B & E) were members of the family True (who are always united in their truths) nor both B & E are from two different families (if they were, then they will fight all the way and won't even agree on one little thing). Thus, B and E must have been lying as members of the family False.
Since we know that they're both lying, then A can only be innocent and E the liar must have been guilty. Furthermore, at least one between C and D must also be guilty by the lies told by E.
Once we knew that E is definitely guilty, then C's first statement checked out, and C's second statement vouched for B's innocence.
From then on, we can clearly see that A's first statement is validated by the truthful C and a lying B (who got caught red-handed with telling lies). By now, we got to know that D is one of the robbers alongside E, too.
With innocents A & B told apart from guilty robbers E & D, it's crystal clear that D has been lying all along and C is another innocent suspect.
So, in conclusion we have
✓ 2 truthful suspects : C & A, and
✓✓ 3 lying suspects : B, E & D, and
✓✓✓ 3 innocent suspects : A, B & C, and
✓✓✓✓ 2 guilty suspects : E & D.
B is the only odd one out ; they even lied as an innocent suspect. When it's something in your blood, you just can't transfuse it all away....
Answer = 11122
The information of the number of guilty robbers amongst the 5 is totally unnecessary though it could be useful in reaching our conclusions.