All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars    
perplexus dot info

Home > Logic > Liars and Knights
House Hindrance (Posted on 2012-11-01) Difficulty: 3 of 5
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 headmanís house number from each of his four acquaintances. They say:
1. It is the sum of squares of two distinct positive integers.
2. It does not have any repeating digits.

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

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

1. It has exactly one digit.
2. It is the product of consecutive prime numbers.
Determine the headmanís house number from these statements.

No Solution Yet Submitted by K Sengupta    
Rating: 4.2500 (4 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
re: A more correct answer (spoiler) | Comment 5 of 9 |
(In reply to A more correct answer (spoiler) by Steve Herman)

You say:
So, 35 is a solution, although I haven't proved uniqueness, either.
You did, since 14,20,27,44,54  do not fit.

  Posted by Ady TZIDON on 2012-11-01 16:47:30
Please log in:
Remember me:
Sign up! | Forgot password

Search body:
Forums (4)
Newest Problems
Random Problem
FAQ | About This Site
Site Statistics
New Comments (5)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Copyright © 2002 - 2020 by Animus Pactum Consulting. All rights reserved. Privacy Information