You are an apprentice at Hyperlogitech Corp. The first thing you learn is every department at Hyperlogitech Corp. has two managers, one of the managers is a Knight, and the other is a Liar. At the first board meeting you attend you ask the managers which department they work for. The responses are as follows:

Fiona: None of Alice, Carol and Eddy are in production.
Alice: Carol is in accounting.
Carol: Eddy and I are in the same department.
Bert:  Dave is the Liar from accounting.
Carol: Fiona is in accounting.
Dave:  At most one of Alice, Carol and Eddy is a liar.
Eddy:  Bert and I are in different departments.
Alice: Fiona is in shipping.

Which managers are in charge of which departments and who are the knights and who are the liars?

If Carol is telling the truth then Eddy is lying; if Eddy is lying he is in the same department as Bert and Carol - which contradicts one of the initial premisses, therefore Carol is a liar.

Fiona is not in accounting.

if(Fiona is not in shipping)Alice is a liar; Carol is not in accounting; Fiona is in Production;
    A-L; B-u; C-L; D-u; E-K; F-u/P;
    Which implies that Dave is a liar.
       therefore: A-L; B-K; C-L; D-L; E-K; F-K/P
           Carol is not in accounting, not in production, therefore  is             in shipping.
            Dave must be in accounting
             A-L; B-K; C-L/S; D-L/A; E-K; F-K/P;
                Eddy as such is in production or accounting.
                   Eddy cannot be in production, Because a Knght is                         already there.
                         Eddy must be in accounting.
                         A-L; B-K; C-L/S; D-L/A; E-K/A; F-K/P;
                         Bert cannot be in accounting or production                                 (Knights already there).  
                            A-L; B-K/S; C-L/S; D-L/A; E-K/A; F-K/P;
                            Therefore A-L/P.
                               Therefore Fiona is a liar; contradiction.
                               Fiona must be in shipping.
                           
                        

                           
                        
               

else Alice is a knight; Carol is in accounting; Fiona is in Shipping
    A-K; B-u; C-L/A; D-u; E-K; F-u/S; 
         Dave was telling the truth.
         Dave cannot be the accounting liar, therefore Bert is a liar.
          A-K; B-L; C-L/A; D-K; E-K; F-L/S
             Eddy is in either shipping or production;
             Bert is in production
             Eddy must be in Shipping
             A-K; B-L/P; C-L/A; D-K; E-K/S; F-L/S
                Since Fiona was lying Alice must be in production
                Dave must be in Accounting.

Alice - Knight/Production
Bert - Liar/Production
Carol - Liar/Accounting
Dave - Knight/Accounting
Eddy - Knight/Shipping
Fiona - Liar/ Shipping

I'm sure I wasted alot of time on the proof that Fiona was in shipping.

Posted by Sam on 2004-11-01 04:01:58