# A Logic Puzzle

1. Jun 3, 2005

### JonF

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. Jun 3, 2005

### neurocomp2003

is it circle only one answer per question?

3. Jun 3, 2005

### neurocomp2003

plz tell me how many i got right cuz pair Q6,17 confused the hell outta me.

Last edited: Jun 3, 2005
4. Jun 4, 2005

### JonF

that is not right, and to tell you how many you got right would be cheating... not that far off though...

5. Jun 4, 2005

### honestrosewater

Hey, you guys are remembering to white out the proposed answers, right? Please? I don't want to accidentally see the answers.

6. Jun 4, 2005

### honestrosewater

Here goes (highlight below for answer):
DAD BED DED ABA DBA DBA BE
The spacing is just for easier reading.

7. Jun 4, 2005

### neurocomp2003

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.

8. Jun 4, 2005

### JonF

good job honestrosewater, how long did it take you?

9. Jun 5, 2005

### honestrosewater

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.

10. Jul 11, 2005

### Ubern0va

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
11. Jul 12, 2005

### honestrosewater

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