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Topic: The mirrored maze 2 (Read 889 times) |
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Leo Broukhis
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The mirrored maze 2
« on: Jul 2nd, 2003, 4:05pm » |
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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).
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| « Last Edit: Jul 2nd, 2003, 4:13pm by Leo Broukhis » |
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James Fingas
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Re: The mirrored maze 2
« Reply #1 on: Jul 3rd, 2003, 7:46am » |
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Very tricky! I found one solution, but it seems like there could be more ... If in doubt, pick "c" 
Small hint: 8 is ambiguous, but I haven't found out what it means.
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Leo Broukhis
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Re: The mirrored maze 2
« Reply #2 on: Jul 3rd, 2003, 8:55am » |
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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).
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| « Last Edit: Jul 3rd, 2003, 8:57am by Leo Broukhis » |
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James Fingas
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Re: The mirrored maze 2
« Reply #3 on: Jul 3rd, 2003, 10:08am » |
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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.
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Leo Broukhis
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Re: The mirrored maze 2
« Reply #4 on: Jul 3rd, 2003, 12:23pm » |
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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.
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James Fingas
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Re: The mirrored maze 2
« Reply #5 on: Jul 3rd, 2003, 12:27pm » |
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Sure it doesn't satisfy all the statements, but I could argue it satisfies statement 8, which demonstrates statement 8's ambiguity.
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Leo Broukhis
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Re: The mirrored maze 2
« Reply #6 on: Jul 3rd, 2003, 1:20pm » |
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Yes, it does. Where's ambiguity?
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James Fingas
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Re: The mirrored maze 2
« Reply #7 on: Jul 4th, 2003, 7:52am » |
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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.
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| « Last Edit: Jul 4th, 2003, 1:23pm by James Fingas » |
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Leo Broukhis
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Re: The mirrored maze 2
« Reply #8 on: Jul 4th, 2003, 12:13pm » |
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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.
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James Fingas
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Re: The mirrored maze 2
« Reply #9 on: Jul 4th, 2003, 1:22pm » |
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Quote:| it is impossible for the least often occurring answer to occur 0 times AND for the question to be answered correctly |
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You admit that babbcbacaa satisfies statement 8, right? Then the least occurring answer is d, occurring zero times. So the impossible has happened?
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Leo Broukhis
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Re: The mirrored maze 2
« Reply #10 on: Jul 4th, 2003, 2:49pm » |
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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.
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Felix
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Number 8 confused me, but using your explanation, I think I have the answer:
babaccadac
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Dante
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Re: The mirrored maze 2
« Reply #12 on: Jul 7th, 2003, 12:50pm » |
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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 babbacadac, 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.
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