Puzzle I

In a certain town, there are two groups of men - one group always tells the truth; the other group always lies.

A stranger arrived in this town and asked one of the natives whether he was a Truth Teller or a Liar. The native answered but the stranger did not catch it. Two other natives, A and B, who overheard the conversation were questioned by the stranger as to what the first man had said. A replied, "He said he was a Truth Teller." Native B replied, "He said he was a Liar."

Can you tell which of the two men, A or B, is a Truth Teller and which is a Liar?

Puzzle II

It was definitely established that 1 of 4 men committed a crime. Following are the statements made by each of the suspects:

• A: B did it.
• B: D did it.
• C: I didn't do it.
• D: B lied when he said I did it.

If only one statement is true, who is the criminal?