A remote island consists of three types of inhabitants. The liars always lie about everything, knights who always tell the truth and, knaves who strictly alternate between lying and telling the truth.

Frank, who is an inhabitant from a nearby island was visiting four acquaintances Abe, Ben, Cal and Don, each of whom are known to Frank to be knaves. Frank wants to meet the newly elected headman at his house. Accordingly, he inquires about the headman’s house number from each of his four acquaintances. They say:

Abe
1. It is the sum of squares of two distinct positive integers.
2. It does not have any repeating digits.

Ben
1. It is even.
2. It has exactly two digits.

Cal
1. It is a prime number.
2. It is one less than a triangular number.

Don
1. It has exactly one digit.
2. It is the product of consecutive prime numbers.

Determine the headman’s house number from these statements.

NOW:   the number is 2

A It does not have any repeating digits.

B  It is even  

 C  It is a prime number

 D  It has exactly one digit.

LATER:Ill  explain  why it is a poor problem and why it is D1 at most.

Took me less than 15 sec to solve it.
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Posted by Ady TZIDON on 2012-11-01 14:19:19