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.

<o:p>After my dinner, I am trying to expand my earlier remarks: </o:p>

<o:p></o:p>

<o:p></o:p>The process of solution went like this: The number cannot be both prime and even, unless it equals 2. Let's check whether 2 fits- bingo - it does! I do not have to look for additional solutions since it's implied the puzzle is uniquely solvable.

As to the plot â€“ there is hardly a reasonable explanation of the cock-and-bull story, telling us about island and 3 types of natives, **while all the participants excluding the solver are knaves.**

The 8 lines introducing the problem remind a gun in act 1, which does not appear in the sequel at all.

Why not start with : **4 persons made 2 statements each- ,one was a total lie and the other represented a true fact**. (less than 20 words, compared with over 80 in the original text!)??

â€¦. Then the 8 statements, and then the request to find the number

** KS â€“ I would appreciate your explanation**.<o:p></o:p>