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A Logic Puzzle

  1. Jun 3, 2005 #1
    This was circulating about the math department last semester and I thought some of you might enjoy it. Good luck.


    The solution to the following puzzle is unique; in some cases the knowledge that the solution is unique may actually give you a short-cut to finding the answer to a particular question, but it's possible to find the unique solution even without making use of the fact that the solution is unique.

    1. The first question whose answer is B is question
    (A) 1
    (B) 2
    (C) 3
    (D) 4
    (E) 5

    2. The only two consecutive questions with identical answers are questions
    (A) 6 and 7
    (B) 7 and 8
    (C) 8 and 9
    (D) 9 and 10
    (E) 10 and 11

    3. The number of questions with the answer E is
    (A) 0
    (B) 1
    (C) 2
    (D) 3
    (E) 4

    4. The number of questions with the answer A is
    (A) 4
    (B) 5
    (C) 6
    (D) 7
    (E) 8

    5. The answer to this question is the same as the answer to question
    (A) 1
    (B) 2
    (C) 3
    (D) 4
    (E) 5

    6. The answer to question 17 is
    (A) C
    (B) D
    (C) E
    (D) none of the above
    (E) all of the above

    7. Alphabetically, the answer to this question and the answer to the following question are
    (A) 4 apart
    (B) 3 apart
    (C) 2 apart
    (D) 1 apart
    (E) the same

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

    9. The next question with the same answer as this one is question
    (A) 10
    (B) 11
    (C) 12
    (D) 13
    (E) 14

    10. The answer to question 16 is
    (A) D
    (B) A
    (C) E
    (D) B
    (E) C

    11. The number of questions preceding this one with the answer B is
    (A) 0
    (B) 1
    (C) 2
    (D) 3
    (E) 4

    12. The number of questions whose answer is a consonant is
    (A) an even number
    (B) an odd number
    (C) a perfect square
    (D) a prime
    (E) divisible by 5

    13. The only odd-numbered problem with answer A is
    (A) 9
    (B) 11
    (C) 13
    (D) 15
    (E) 17

    14. The number of questions with answer D is
    (A) 6
    (B) 7
    (C) 8
    (D) 9
    (E) 10

    15. The answer to question 12 is
    (A) A
    (B) B
    (C) C
    (D) D
    (E) E

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

    17. The answer to question 6 is
    (A) C
    (B) D
    (C) E
    (D) none of the above
    (E) all of the above

    18. The number of questions with answer A equals the number of questions with answer
    (A) B
    (B) C
    (C) D
    (D) E
    (E) none of the above

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

    20. The answer to question 20 is
    (A) E
    (B) E
    (C) E
    (D) E
    (E) E
     
    Last edited: Jun 3, 2005
  2. jcsd
  3. Jun 3, 2005 #2
    is it circle only one answer per question?
     
  4. Jun 3, 2005 #3
    Answer:DADBEBBEDADADBADBADE
    plz tell me how many i got right cuz pair Q6,17 confused the hell outta me.
     
    Last edited: Jun 3, 2005
  5. Jun 4, 2005 #4
    that is not right, and to tell you how many you got right would be cheating... not that far off though...
     
  6. Jun 4, 2005 #5

    honestrosewater

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    Gold Member

    Hey, you guys are remembering to white out the proposed answers, right? Please? I don't want to accidentally see the answers. o:)
     
  7. Jun 4, 2005 #6

    honestrosewater

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    Gold Member

    Here goes (highlight below for answer):
    DAD BED DED ABA DBA DBA BE
    The spacing is just for easier reading.
     
  8. Jun 4, 2005 #7
    yeah i messed up 4 Qs ...don't think i messed up anymore
    Q6, 17 really messed me up but honestrosewater answer doesn't make sense either for them. I couldn't figure out how there could be a solutionf or the 2.
     
  9. Jun 4, 2005 #8
    good job honestrosewater, how long did it take you?
     
  10. Jun 5, 2005 #9

    honestrosewater

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    Gold Member

    I had 6 & 17 backwards the first time, but 2 made me check it again. It makes sense to me now. It took me ~90 minutes, but I was very tired and would completely forget what I was doing every five minutes. :tongue2: I was just determined to finish before going to bed.
     
  11. Jul 11, 2005 #10
    Wow, its like the ultimate riddle, based entirely on relative answers. I'm gonna pass this around to my friends if you dont mind. :)

    I have a pretty good idea about how to do this but I know that once I start I won't be able to stop, and I have other things to do today.

    To help you out a bit neuro, I think the 6-17 answer has a computer programming background. It's quite obvious if you consider the fact that honestrosewater had them backwards for a while (that should be a hint, the fact that they appear interchangeable unitll you answer other questions). If you want I can go into more detail via PM.
     
    Last edited: Jul 11, 2005
  12. Jul 12, 2005 #11

    honestrosewater

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    Gold Member

    FYI: Figuring out the number of questions with answers A, B, etc. was a big help for me in eliminating other options.
     
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