Joe is either a knight, a liar, or a knave. His favorite number is an integer between 1 and 1000. He makes the following statements about his favorite number:

1. It is odd.
2. It is divisible by 7.
3. It is divisible by 23.
4. It is not divisible by 19.
5. It has an even number of divisors.
6. It ends in 9.

What type is Joe, and what is his favorite number?

n=23*19=437
Joe is a knave ,

 the number is odd ?  (YES).

 divisible by ? ?      (NO), 

divisible by 23 ?     (YES), 

NOT divisible by 19 ?     (NO),  =(NOT not divisible)

, not a square ?(YES),     ,- only  squares have od # of divisors

 ends by digit 9 ?     (NO).

Posted by Ady TZIDON on 2011-04-27 11:54:04