Four men (Andy, Ben, Cal, and Dan) eat dinner together at a square table in a restaurant. Suddenly, Andy cries out "I've been poisoned" and falls over dead. Andy's companions were questioned by the police and each made three statements, exactly one of which is false for each man, which are as follows:
1. I didn't do it.
2. I was sitting next to Dan.
3. We had our usual waiter today.
1. I was sitting across from Andy.
2. We had a new waiter today.
3. The waiter didn't do it.
1. Cal didn't do it.
2. The waiter poisoned Andy.
3. We had a new waiter today.
Assuming that only Andy's companions and the waiter are implicated, who is the murderer?