Tricky (math?) Riddle ?

Question

This was on my math worksheet...

Four men were eating dinner together in a restaraunt when Smith cried out, "I've been poisoned!" and fell dead. His dinner company was taken into questioning. Each made three statements, and each person told one lie and two truths. If the dinner companions and the waiter are the ONLY suspects, who should the police arrest for murder?

WATTS: I didn't do it.

I was sitting next to O'Neil

We had our usual waiter

ROGERS: I was sitting across from Smith

We had a new waiter today

The waiter didn't do it

O'NEIL: Roger's didn't do it

It was the waiter.

Watts lied when he said we had our usual waiter.

Any help would be appreciated, since I can't figure it out.

I think Roger didn't do it, since two people siad he didn't, I think there was a new waiter, and I do believe the waiter did it, since Rogers could have lied and then O'Neil would have been honest...but then what did O'Neil lie about???

Answer 1

It was O'Neil.  Here's why:

This way it all works out and there are no contradictions.

If Watts is lying about the waiter being usual, then Rogers and O'Neil are telling the truth about it.  So then we can believe the other 2 things Watts says, which are "Watts is next to O'Neil" and "Watts didn't do it."

If those 2 things are true, then we know Rogers is lying when he said he was sitting across from Smith.  So the rest of what he said is true, i.e. "The waiter didn't do it."

If that is true, then O'Neil is lying about the waiter having done it, and is telling the truth about Watts lying and "Rogers didn't do it."

That means we know that Watts, Rogers, and the Waiter didn't do it.  The only one left is O'Neil.

Arrest that man!

Answer 2

True - WATTS: I didn't do it.

True - WATTS: I was sitting next to O'Neil

False - WATTS: We had our usual waiter

False - ROGERS: I was sitting across from Smith

True - ROGERS: We had a new waiter today

True - ROGERS: The waiter didn't do it

True - O'NEIL: Roger's didn't do it

False - O'NEIL: It was the waiter.

True - O'NEIL: Watts lied when he said we had our usual waiter.

O'Neil did it.

To give you an idea how I worked it out...

Firstly I assumed that O'Neil was lying about Watts' lie and then followed the logic through and ended up with Rogers' not lying about anything.  So then I asssumed that O'Neil was telling the truth about Watts' lie and then followed that logic through...

If Watts 3rd statement is a lie then we know that Watts didn't do it and that he was sitting next to O'Neil.  We also know that they had a new waiter.

So then looking at Rogers' statements we know that the 2nd one is true and we know that if Watts and O'Neil are sitting next to each other then Rogers and Smith were not sitting across from each other.  So then we know that the waiter didn't do it.

Then looking at O'Neil's answers if statement 2 is false and 3 is true then the 1st statement is true too.

So we know that Watts' didn't do it, the waiter didn't do it and Rogers didn't do it... That leave us with O'Neil did it.