First, ask the same question twice :
1) "Is the belt in the left hand box?"
2) "Is the belt in the left hand box?"
if you get two answers the same you know they are both false answers
- Two "No"s means the belt is in the left box so you can open it.
- Two "Yes"s means it isn't in the left hand box but you have a true and a false answer left so your next question should be :
- 3) "if my fourth question was whether the belt is in the right hand box what would you answer?" - he either tells the truth about his final answer (which is a lie) or a lie about his final answer (which is the truth) so this will always be a lie - so a "yes" means you can open the middle box and a "no" means you can open the right hand box
if you get different answers to 1 and 2 then you know you have had the one True answer allowed so you ask:
- Is the belt in the right hand box? - if he says No as he must be lying then open the right hand box, otherwise :
- is the belt in the middle box? - if he says No as he must be lying then open the middle box, otherwise open the left hand one.