Whodunnit?

[bonanova]

Ed is dead.

You question four suspects, of which one is guilty.

Each suspect makes exactly one false statement and exactly one true statement.

• Alex: I did not kill Ed. Either Bob is the killer or none of us is.
• Bob: I did not kill Ed. Duke is the killer.
• Chuck: I did not kill Ed. Bob is lying when he says Duke is the killer
• Duke: I did not kill Ed. If Alex did not kill him, then Bob did.

Whodunnit?

[Pickett]

Chuck

For brevity's sake, let's even ignore the original part of the OP that says "of which one is guilty" and first assume that no one killed Ed.

This means that everyone's first statement ("I did not kill Ed") is true for everyone. But since none of them killed Ed, Alex's second statement would also be true...which means he told 2 truthful statements...therefore, SOMEONE killed Ed.

If Alex killed Ed:

• This means that Alex's first statement is FALSE...which means his second statement must be TRUE. However, his second statement is in fact FALSE, because Bob didn't kill Ed and one of them did. Therefore Alex didn't kill Ed.

If Bob killed Ed:

• This means that Alex's first statement is TRUE...which means his second statement must be FALSE. However, it is in fact TRUE, because Bob did kill Ed. Therefore Bob did not kill Ed.

If Duke killed Ed:

• Bob's first statement is TRUE...which means his second statement must be FALSE. However, it is in fact TRUE because Duke did kill Ed. Therefore Duke did not kill Ed.

If Chuck killed Ed:

• Alex's first statement is TRUE, which means his second statement must be FALSE...this is accurate because Bob didn't kill Ed AND one of them did.
• Bob's first statement is TRUE, which means his second statement must be FALSE...this is accurate because Duke didn't kill Ed.
• Chuck's first statement is FALSE, which means his second statement must be TRUE...this is accurate because Bob is lying when he said Duke killed Ed (as previously shown above).
• Duke's first statement is TRUE, which means his second statement must be FALSE...this is accurate because Alex didn't kill Ed, but neither did Bob...

Therefore Chuck is the killer.

Edited June 12, 2014 by Pickett