Can you score 100% on this ten-question Self-Referential Quiz, and can you prove in a few words why there...

logic/self.ref.quiz New

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Problem

Can you score 100% on this ten-question Self-Referential Quiz, and can
you prove in a few words why there is only one solution?

1. The first question whose answer is A is question
   (A) 4   (B) 3   (C) 2   (D) 1   (E) none of the above

2. The only two consecutive questions with identical answers are questions
   (A) 3 and 4   (B) 4 and 5   (C) 5 and 6   (D) 6 and 7   (E) 7 and 8

3. The next question with answer A is question
   (A) 4   (B) 5   (C) 6   (D) 7   (E) 8

4. The first even numbered question with answer B is question
   (A) 2   (B) 4   (C) 6   (D) 8   (E) 10

5. The only odd numbered question with answer C is question
   (A) 1   (B) 3   (C) 5   (D) 7   (E) 9

6. A question with answer D
   (A) comes before this one
   (B) comes after this one
   (C) comes before and after this one
   (D) comes neither before nor after this one
   (E) none of the above

7. The last question whose answer is E is question
   (A) 5   (B) 6   (C) 7   (D) 8   (E) 9

8. The number of questions whose answers are consonants is
   (A) 7   (B) 6   (C) 5   (D) 4   (E) 3

9. The number of questions whose answers are vowels is
   (A) 0   (B) 1   (C) 2   (D) 3   (E) 4

10.The answer to this question is
   (A) A   (B) B   (C) C   (D) D   (E) E

-- Martin Henz <henz@dfki.uni-sb.de>, "SRQ: Another SRAT" (May 1996)

[ Editor: the opening sentence combines Henz's two questions, "Can you
score 100%?  Can you prove in a few words, why there is only one
solution?" ]

Show solution

In the SPOILER which follows, i can show TWO solutions.  This seems to
disprove the "one solution" theory.  i believe there are only two
solutions.  i'm not sure what Martin would call a proof, but after
working through it, it seems obvious.

ObPuzzle:  Beat my time of 2:45.  That doesn't count a cursory
read-through i gave it a few hours before sitting down to think about
it.

Two possible solutions:

ABCDXXXCABBABEBEDXX
ABCDXXXCABBADEBEBXX

Note that the only difference between these two is in questions 6 and
10.  These don't seem to be affected by any of the other questions
(except for the consonant/vowel ones, which a B/D flip doesn't affect.)

-- Stan Guthrie <gsg5501@msu.oscs.montana.edu>

[ Editor: the quiz has 10 questions but each string above has 19
letters; the posting does not explain how to read them. ]

[ Editor: another reply to Martin Henz's posting of the quiz, May 1996.
The quiz was introduced as "SRQ: Another SRAT", following Henz's
earlier Self-Referential Aptitude Test. ]

I can score 100%, but I see more than one solution.

Here's the part that I'm certain of...

1) C
2) A
3) B
4) B
5) A
6)
7) E
8) B
9) E
10)

6 and 10 can be either B/D, D/B or D/C to score 100%.  I'll bet that you
meant for the first one to be the correct answer, though....

My reasoning for the whole kit-n-caboodle: (don't know that it's the
shortest....)

8/9 must be either A/D or B/E, so 5 isn't D or E.  6 isn't E because
choices A, B, and D are complete.  8 isn't E.  Therefore, 7 can only be
E, which makes 8 B and 9 E.

1 isn't D.  2 isn't D or E.

3 isn't D or E.  If 3 were A, then 4 would be A, which leaves no correct
answer for 2.  If 3 were C, then 6 would be A, 5 would be B, 4 would be
D, which also leaves no correct answer for 2.  Therefore, 3 is B.

5 is A.  1 is C.  2 is A.  4 is B.

2, 5, 7, and 9 are all vowels, so we know that 6 and 10 are both
consonants.  We also know that 6 is not C, but that's all the
conclusions we can make specifically (except that if 6 were B then 10
would have to be D).

Another great puzzle!  This one didn't take nearly as long as the last,
but the SRAT hurt my brain too much anyway!! :-)

-- Matthew Daly <daly@PPD.Kodak.COM>