Mr. Matthews has just joined Ace Company as its new financial officer, in charge of a group of six accountants: Betty, Bob, Ed, Frank, Gladys, and Marsha.  The departing financial officer has confided to him that two of the six accountants are crooks; also that two of them always lie, two always tell the truth, and two alternate between lies and truth (and are therefore neither liars nor truthful).  Unfortunately, he has refused to name names since it is no longer his problem.

    Mr. Matthews must now figure out who the crooks are.  He has devised a cunning plan: he has asked each accountant to slip him a confidential note containing two or three statements about the thefts and about the other accountants.  Help Mr. Matthews wade through the conflicting statements he has gotten back from his accountants and identify the crooks.

Betty:  1.  No women are crooks.

            2.  Gladys and Marsha are liars.

Bob:  1.  Betty is a crook, but I am not.

          2.  One of the women is a liar.

Ed:  1.  Marsha is a crook, but I am not.

       2.  Frank tells the truth.

       3.  Marsha lies half the time.

Frank:  1.  Gladys is a crook, but I am not.

             2.  Bob is a liar.

Gladys:  1.  Betty isn’t truthful.

               2.  Ed is not a crook.

Marsha:  1.  Gladys is a liar.

                2.  Frank is not a crook.

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