In the city of Enigmamia every person is either a knight or a liar. One night, two robbers managed to break into the Enigmamia Central Bank.

Five men were brought to the police station for questioning. It was certain both robbers were present. To narrow the field, each man was individually interrogated about the identities of the robbers. The results were:

Alex: 1. At most one of Bill and Eddy is guilty. 2. Dave is guilty.

Bill: 1. Both Alex and Carl are guilty. 2. Eddy is not guilty.

Carl: 1. At least one of Dave and Eddy is guilty. 2. Bill is not guilty.

Dave: 1. Exactly one of Alex and Bill is guilty. 2. Carl is guilty.

Eddy: 1. Neither Carl nor Dave is guilty. 2. Alex is guilty.

Which two suspects robbed the bank?

Let's look at each man's pair of statements.

The only way Alex's first statement is false is if Bill and Eddy are both guilty.
If this is not the case, his first (and therefore both) statement is true, and Dave is guilty.
Therefore, we have only two cases for the guilty parties, based on the fact that Alex is either a knight or a liar:
1. Bill & Eddy
2. Dave & ??

Looking at Bill's statements, his first will only be true if Alex and Carl are both guilty.
If that is not the case, then the second statement is false, as well, and Eddy is guilty.
Therefore, there are two possible cases for the guilty parties based on Bill's statements:
1. Alex & Carl
2. Eddy & ??

Combining these two conclusions, we see that there are only two possiblities for the robbers:
1. Bill & Eddy
2. Dave & Eddy
Either way, Eddy is guilty, and his partner in crime was Bill or Dave.

Carl's first statement, then, must be true, since we know Eddy is guilty.
Therefore, he is a knight, and his second statement is true as well, so Bill is not guilty.

We can stop there; as we know that Dave and Eddy are the guilty parties.

Continuing on, we see that Dave is a liar, as is Eddy.

Altogether, the robbers are Dave and Eddy.
Alex and Carl are knights; Bill, Dave, and Eddy are liars.

Posted by DJ on 2003-06-27 09:14:39