This logic puzzle was created by Mu Alpha Theta.
Each question in this puzzle has a unique answer. Good luck.
It is recommended that you set aside about a half hour to solve this.
If you want to warm up with another selfreferential logic puzzle, try this one.
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85  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 answer E is
(A) 0 (B) 1 (C) 2 (D) 3 (E) 4
4. The number of questions with 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 these answers
(E) All of these answers
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) Even
(B) Odd
(C) A perfect square
(D) 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 these answers
(E) All of these answers
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 these answers
19. The answer to this question is
(A) A (B) B (C) C (D) D (E) E
20. What is 1+1 in base 1337?
(A) 3 (B) . (C) 1 (D) 4 (E) 2

\[ \]
Let \(\mathcal{A}\) represent the sum of the numbers of the questions with answer \(A;\) \(\mathcal{B}\) for the sum of the numbers questions with answer \(B;\) and so on, up to \(\mathcal{E}\).
Find \(\mathcal{A}+2\mathcal{B}+3\mathcal{C}+4\mathcal{D}+5\mathcal{E}.\)
Details and Assumptions:
If questions 3, 13, 15, and 16 have answer \(Z,\) then \(\mathcal{Z}=3+13+15+16=47\)