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.
Answer...
