# Self-Referential Logic Puzzle

Logic Level 4

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 self-referential logic puzzle, try this one.

  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 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 $$\mathcal{Z}=3+13+15+16=47$$

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