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A little puzzle for you to have a think about - 1 to 5
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Demian*
Oh Lordy, Plegaleggole
Sat 20th Sep '08 6:28PM
4678 Posts
Demian's Avatar
Member Since
7th Apr '03
...because I think my brain just started melting.


Instructions:
- Answer all 20 questions (each with a letter from A to E).
- Wherever a question refers to an answer or answers, it means
YOUR answers, not some hypothetical "best" or "right" answers.
- Your score is the number of questions whose answers are correct.
- Your goal is to achieve as high a score as possible.

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

2. The next question with the same answer as this one is:
(A) 4
(B) 6
(C) 8
(D) 10
(E) 12

3. The number of questions whose answer is D is:
(A) 2
(B) 3
(C) 4
(D) 5
(E) 6

4. The answer to this question is the same as the answers
to questions:
(A) 6 and 13
(B) 11 and 16
(C) 7 and 20
(D) 1 and 15
(E) 9 and 12

5. The answer to question 14 is:
(A) B
(B) E
(C) C
(D) A
(E) D

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

7. The answer that appears most often is:
(A) A
(B) B
(C) C
(D) D
(E) E

8. Ignoring those that occur equally often, the answer that
appears least often is:
(A) A
(B) B
(C) C
(D) D
(E) E

9. The other questions with the same answer as this one, not counting
any whose answers are wrong, have numbers whose sum is in the range:
(A) 39 to 43, inclusive
(B) 44 to 48, inclusive
(C) 49 to 53, inclusive
(D) 53 to 57, inclusive
(E) 54 to 58, inclusive

10. The answer to question 17 is:
(A) D
(B) B
(C) A
(D) E
(E) wrong

11. The only two consecutive questions with identical answers
are questions:
(A) 15 and 16
(B) 16 and 17
(C) 17 and 18
(D) 18 and 19
(E) 19 and 20

12. The number of OTHER questions with the same answer as this
one is the same as the number of questions with answer:
(A) B
(B) C
(C) D
(D) E
(E) none of the above

13. The number of questions whose answer is E is:
(A) 5
(B) 4
(C) 3
(D) 2
(E) 1

14. No one answer appears exactly:
(A) two times
(B) three times
(C) four times
(D) five times
(E) none of the above

15. The only odd-numbered question with answer A is:
(A) 7
(B) 9
(C) 11
(D) 13
(E) 15

16. The answer to question 8 is the same as the answer to
question:
(A) 3
(B) 7
(C) 13
(D) 18
(E) 20

17. The answer to question 10 is:
(A) C
(B) D
(C) B
(D) A
(E) correct

18. The number of prime-numbered questions whose answers
are vowels is:
(A) a prime number
(B) a square number
(C) an odd number
(D) an even number
(E) zero

19. The last question whose answer is B is:
(A) 14
(B) 15
(C) 16
(D) 17
(E) 18

20. The maximum score that can be achieved on this test is:
(A) 18
(B) 19
(C) 20
(D) indeterminate
(E) achievable only by getting this question wrong

  

Epicure_mammon
I'm not crazy cause I take the RIGHT pills :)
Sun 21st Sep '08 11:05PM
140 Posts
Epicure_mammon's Avatar
Member Since
12th Dec '06
And once you've solved it you should have a read of this:

http://consc.net/misc/moser.html

that said, the link was down earlier - so I had to read it through the cache:


http://64.233.183.104/search?q=cache:lAJsYMmsAfMJ:consc.net/misc/moser.html+self+referencial+story&hl=en&ct=clnk&cd=1&gl=uk
  

Spanners*
Misses his big brother :(
Mon 22nd Sep '08 7:59PM
4597 Posts
Spanners's Avatar
Member Since
7th Apr '03
Whoa it's like doing 20-way simultaneous equations. I thought I was getting somewhere until I saw question 10. How can the answer to a question be wrong? Or are they just messin with my head?
    

Amanshu*
Giggity Giggity goo
Tue 23rd Sep '08 9:49AM
2708 Posts
Amanshu's Avatar
Member Since
25th Aug '04


Spanners was bold enough to comment:
Whoa it's like doing 20-way simultaneous equations. I thought I was getting somewhere until I saw question 10. How can the answer to a question be wrong? Or are they just messin with my head?



You need to look at it in conjunction with question 17... They refer to each other, so it's possible to get one right and one wrong...
   

Epicure_mammon
I'm not crazy cause I take the RIGHT pills :)
Tue 23rd Sep '08 1:15PM
140 Posts
Epicure_mammon's Avatar
Member Since
12th Dec '06
This is a quite significant extension of a problem posed by Jim Propp called the Self Referential Aptitude Test. It only has 10 questions and there's no concept of "Wrongness" - that is - there is definitely at least one perfect solution. The original set of questions is:


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

2. Identical answers have 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, but not after (B) comes after this one, but not before (C) comes before and after this one (D) does not occur at all (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) (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

The Extension, cited originally by Don Woods implies that there may not exist a perfect solution. Therefore the problem is changed from a simple example of predicate logic, to an optimisation problem across a "Score" function. That said - Don Woods himself believes that there is exactly one solution, but has evidently not yet proved it:

http://www.icynic.com/~don/20qintro.html
  

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