I didn't kill Mack

[BMAD]

Mack "The Knife", the notorious tough guy, was found murdered one night in an alley behind the nightclub he usually frequented.  The police brought in three suspects the morning after.  That afternoon a police investigator interrogated the three men.  They made the following statements.

 

Bud:

1. I didn't kill Mack.

2. Jack is not my friend.

3. I knew Mack.

 

Jack:

1. I didn't kill Mack.

2. Bud and Tug are friends of mine.

3. Bud didn't kill Mack.

 

Tug:

1. I didn't kill Mack.

2. Bud lied when he said that Jack was not his friend.

3. I don't know who killed Mack.

 

Only one of the three is guilty, and only one of each man's statements is false.  who killed Mack the Knife?

[gavinksong]

It's not Bud because if it was, Bud 1 and Jack 3 would both be false, which would make Bud 2 and Jack 2 both true which is a contradiction.

 

It's not Tug because if it was, Tug 1 and Tug 3 would both be false, which isn't possible.

 

So it must be Jack.