A crime has been committed and there are ten suspects. Precisely one of the suspects is a knight and the remaining nine are liars.
George said Arthur did it, Arthur said Bill did it, Bill said Chuck did it, Chuck said Fred did it, Eddie said Fred did it so Fred confessed and said that he did do it.
Harry said Eddie did it, Dave then confessed that he did do it- so John also confessed and said that he did it. Finally, Ian said that he didn't do it.
If George didn't do it, one of the ten suspects did do it - who committed the crime?
Suppose George did not do it. Then, one of the other people did it. If Ian did it, then everybody is a liar. Therefore, Ian did not do it, so he is a knight. That makes all of the other suspects liars. Therefore, nobody accused did it. The only person other than George and Ian who was not accused is Harry, so Harry did it. Therefore, if George did not do it, then Harry did it.
Suppose George did it. If Ian did not do it, then he is a knight. Therefore, as we have seen, Harry is the only other person who could have done it. If Ian did it, then he is a liar. There is only one knight, so the other person who did it was only accused by one person. They could be Arthur, Bill, Chuck, Dave, Eddie, or John. Therefore, there are 9 solutions.
George, Ian, Arthur
George, Ian, Bill
George, Ian, Chuck
George, Ian, Dave
George, Ian, Eddie
George, Ian, John
Posted by Math Man
on 2013-08-22 16:43:59