The secretary at a computers company is pregnant! It may have been one of the three partners' fault, or maybe someone else's. If a partner was the guilty party, he knows it... but he doesn't want the others to know it was him.

The three partners agree that they must know whether it was one of them who made the girl pregnant (thus possibly allowing a suit against the company) or if it was someone else.

How can they decide if one of them is to blame, without anybody having to accept being the father, if that was the case?

(Some notes: They might just write on papers either "I DID IT" or "I WASN'T IT", but the handwriting might give the guilty party away. Putting a white or black marble in an urn (white=innocent, black=guilty) might work, but someone could possibly see what color was being put in; also, if the guilty one went first, the second could peek inside and realize the answer. The optimum solution should not require much --or any-- extra equipment, and should "resist" inquisitive partners. And, of course, being all of them quite capable hackers, computers are out of the question!)

Partners Bill, Teddy and Gary are alone together in a large conference room in the office. Gary is 30 feet from Bill and Teddy. Secretary Monica is away from the office, conferring with her lawyer.

Bill enters the number 100 on a calculator, and hands it to Teddy. Only Bill and Teddy know that the original number is 100. Teddy mentally computes the sum of 100 plus  the number of partners he knows to be innocent, then purges the calculator's memory and enters that sum. He then walks 30 feet over to Gary and hands him the calculator. Gary mentally computes the sum of the number on the calculator and the number of partners he knows to be innocent, purges the calculator's memory, enters that sum, and walks 30 feet back to Bill and hands it back to him.

If Teddy is guilty, he puts 102 on the calculator. Gary sees that the number is 102, but doesn't know whether the original number was 100 or 101, so he doesn't know whether Teddy is guilty. Gary puts 103 on the calculator. Bill sees that the number is 103, which confirms that one of Gary and Teddy is guilty. Bill announces that one of the partners is guilty.

If Gary is guilty, Teddy puts 101 on the calculator. Gary sees that the number is 101, and since he knows that he himself is guilty, he surmises that the original number was 100. Gary puts  103 on the calculator. Bill sees 103 and knows that one of Teddy and Gary is guilty.  Bill announces that one of the partners is guilty.

If Bill is guilty, Teddy puts 101 on the calculator. Gary sees that the number is 101, but doesn't know whether the original number was 100 or 99, and so does not know whether Teddy is guilty or not. Gary puts 102 on the calculator. Bill sees that the number is 102, as he knew it would be, and since he knows that he himself is guilty, he announces that one of the partners is guilty.

If none are guilty, Teddy puts 101 on the calculator. Gary sees that the number is 101, but doesn't know whether the original number was 100 or 99, and so does not know whether Teddy is guilty or not. Gary puts 102 on the calculator. Bill sees that the number is 102, and since he knows that he himself is innocent,  he now announces that none of them is the father of Monica's baby.

     

      

 

 

 

 

 

 

 

 

 

Edited on February 21, 2004, 10:06 pm

Posted by Penny on 2004-02-21 19:38:34