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        riddles >> hard >> The mirrored maze 2
        
(Message started by: Leonid Broukhis on Jul 2^nd, 2003, 4:05pm)

Title: The mirrored maze 2
Post by Leonid Broukhis on Jul 2^nd, 2003, 4:05pm

1. Answers to questions 3, 4, and 5 are:
a) the same
b) all different
c) 'a' occurs twice
d) another letter occurs twice

2. The number of answers 'a' is:
a) unique
b) the same as the number of answers 'd'
c) the same as the number of answers 'b'
d) the same as the number of answers 'c'

3. The number of answers 'd' is:
a) 0
b) 1
c) 2
d) 3

4. The first question with the answer 'c' is:
a) 5
b) 4
c) 3
d) 2

5. The answer to this question is the same as to
a) 8
b) 9
c) 10
d) none of the above or more than one of the above

6. The number of answers 'b' is greater than the number of
answers:

a) a
b) c
c) d
d) none of the above or more than one of the above

7. The unique most often occurring answer is:
a) a
b) b
c) c
d) none of the above

8. The least often occurring (but present) answer is:
a) a
b) b
c) c
d) d

9. The total number of answers 'b', 'c', or 'd' (consonants) is:
a) even
b) odd
c) prime
d) square

10. The answers to the following two questions are the same:
a) 3 and 4
b) 4 and 5
c) 5 and 6
d) 6 and 7

(Corrected typos).

Title: Re: The mirrored maze 2
Post by James Fingas on Jul 3^rd, 2003, 7:46am

Very tricky! I found one solution, but it seems like there could be more ... If in doubt, pick "c" ;)

Small hint: [hide]8 is ambiguous, but I haven't found out what it means.[/hide]

Title: Re: The mirrored maze 2
Post by Leonid Broukhis on Jul 3^rd, 2003, 8:55am

As answers to question 8 are self-referential, the parenthetical is redundant. It is a joke. And the solution is unique (verified by my favorite method).

Title: Re: The mirrored maze 2
Post by James Fingas on Jul 3^rd, 2003, 10:08am

But what if you had babbcbacaa? The answer to 8 is c), which could be considered valid because c is still the answer (that is present) that occurs the least.

Title: Re: The mirrored maze 2
Post by Leonid Broukhis on Jul 3^rd, 2003, 12:23pm

James,

babbcbacaa does not work because the number of answers 'a' is not unique - it is the same as of 'b' (4), which contradicts question 2.

Title: Re: The mirrored maze 2
Post by James Fingas on Jul 3^rd, 2003, 12:27pm

Sure it doesn't satisfy all the statements, but I could argue it satisfies statement 8, which demonstrates statement 8's ambiguity.

Title: Re: The mirrored maze 2
Post by Leonid Broukhis on Jul 3^rd, 2003, 1:20pm

Yes, it does. Where's ambiguity?

Title: Re: The mirrored maze 2
Post by James Fingas on Jul 4^th, 2003, 7:52am

The statement "The least often occurring (but present) answer is:" is ambiguous, because I can't be sure which of these it means:

1) (The least often occuring answer is:) AND (Aside: the least often occuring answer is present, of course)

2) (The least often occuring answer that actually occurs is:)

One interpretation allows some answers to not occur, and the other doesn't. It seems to me that only 1) is funny.

Title: Re: The mirrored maze 2
Post by Leonid Broukhis on Jul 4^th, 2003, 12:13pm

James, it look like you still haven't got the joke. As the answers to question 8 are self-referential, it is impossible for the least often occurring answer to occur 0 times AND for the question to be answered correctly not because of the wording of the question, but because of the way the multiple choice is presented.

Title: Re: The mirrored maze 2
Post by James Fingas on Jul 4^th, 2003, 1:22pm

Quote:

it is impossible for the least often occurring answer to occur 0 times AND for the question to be answered correctly

You admit that babbcbacaa satisfies statement 8, right? Then the least occurring answer is d, occurring zero times. So the impossible has happened?

Title: Re: The mirrored maze 2
Post by Leonid Broukhis on Jul 4^th, 2003, 2:49pm

babbcbacaa satisfies question 8 in its original form, and does not satisfy it if you remove the parenthetical. So, one way or another, the parenthetical is enforced.

Title: Re: The mirrored maze 2
Post by Felix on Jul 6^th, 2003, 5:14pm

Number 8 confused me, but using your explanation, I think I have the answer:

[hide]babaccadac[/hide]

Title: Re: The mirrored maze 2
Post by Dante on Jul 7^th, 2003, 12:50pm

You beat me to it, Felix. I wrote a little Java program to calculate the answer for me, cos it seemed easier than trying to solve it by hand. It came up with [hide]babbacadac[/hide], and confirmed that there is only a single answer.

Just for the sake of it, I've uploaded it to http://www.danieltebbutt.com/mirroredmaze.java

FYI, it took somewhat less than 1 second to search every possible combination and find the only one to match all 10 requirements.