Who stole the money? Two people among Bill, Dan, Phil, Amy, Chris, and Mike stol

Question

Who stole the money? Two people among Bill, Dan, Phil, Amy, Chris, and Mike stole the money. Each was questioned about the money and responded as follows: Bill: Chris and Amy stole it. Dan: Phil and Mike stole it. Phil: Mike and Chris stole it. Amy: Bill and Chris stole it. Chris: Phil and Dan stole it. Mike was unavailable for comment. We know that four of the above statements are true about one of the guilty parties, and one lied about both. Who stole the money? Support your conclusion with a logical proof, or explain why it cannot exist.

Explanation / Answer

The letters in the sebsequent answers are the initials of the names,

Bill - B, Dan - D, Phil - P, Amy - A, Chris - C, Mike - M

Statements Made:

B - C A | D - P M | P - M C | A - B C | C - P D

According to B, C and A are guilty, Assuming C to be guilty, we are sure that A M B are not guilty, which leaves P D on the doubt. If P is guilty then none the person lied about both, thus D is guilty.

This answer satisfies the conditions, i.e. B P A C spoke truth about one of the guilty parties and D lied about both.

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