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The Barg's Self-Referential Logic Puzzle - Difficult

The following questions refer only to themselves and each other. No outside knowledge is required, but that does not make it easy. Good luck!
[A] denotes the total quantity of questions whose answer is A. Likewise for [B], [C], [D], and [E].
All truth values are exclusive, ie, in no question is there more than one correct answer.
Quiz by itsthebarg
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Last updated: March 9, 2024
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First submittedMarch 9, 2024
Times taken8
Average score76.0%
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1. [A] = ?
(A) 6
(B) 7
(C) 8
(D) 9
(E) 10
Minimizing 1 and 2 maximizes 6.
2. [B] = ?
(A) 2
(B) 3
(C) 4
(D) 5
(E) 6
Minimizing 1 and 2 maximizes 6.
3. [C] = ?
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
5 gives [E] = 7, and these are given in 6-8 and 13-16. 2 gives [B] = 2, and these are given in 11 and 25.10, 17, and 21 are all C. 3C would contradict itself.
4. [D] = ?
(A) 4
(B) 5
(C) 6
(D) 7
(E) 8
3D and 7E imply 4C
5. [E] = ?
(A) 7
(B) 8
(C) 9
(D) 10
(E) 11
Given 6, [C] + [D] + [E] must be 17. This is the minimum from 5 and 7.
6. [A] + [B] = ?
(A) 4
(B) 5
(C) 6
(D) 7
(E) 8
Minimizing 1 and 2 maximizes 6.
7. [C] + [D] = ?
(A) 14
(B) 13
(C) 12
(D) 11
(E) 10
Given 6, [C] + [D] + [E] must be 17. This is the minimum from 5 and 7.
8. Which set includes 3 unique answers?
(A) None of the below
(B) {5,6,7}
(C) {6,7,8}
(D) {7,8,9}
(E) {8,9,10}
B and C are ruled out by 6 and 7. 9 contradicts D. A contradicted by 9 and 10.
9. What is the answer to question 13?
(A) B
(B) C
(C) D
(D) E
(E) A
From 10.
10. What is the answer to question 9?
(A) B
(B) C
(C) D
(D) E
(E) A
15 rules out E, A (from 5), and B (from 25). D implies 9E, which is contradicted by 16.
11. What is the answer to question 10?
(A) B
(B) C
(C) D
(D) E
(E) A
From 10.
12. What is the answer to question 11?
(A) B
(B) C
(C) D
(D) E
(E) A
From 11.
13. What is the answer to question 12?
(A) B
(B) C
(C) D
(D) E
(E) A
From 12.
14. Questions 14, 15, and 16 all share which answer?
(A) A
(B) B
(C) C
(D) D
(E) E
From 16.
15. How many unique answers exist in the set {5,10,15,20,25}?
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
From 14.
16. How many unique answers exist in the set {1,4,9,16,25}?
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
From 25.
17. How many unique answers exist in the set {18,19,20,21,22,23,24}?
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
5 gives [E] = 7, and these are given in 6-8 and 13-16. 2 gives [B] = 2, and these are given in 11 and 25. A, C, and D are all already found in this set. Thus, 3.
18. What is the most common answer in the set {3,6,9,12,15,18,21,24}?
(A) A
(B) B
(C) C
(D) D
(E) E
Among other multiples of 3, there are 3 Ds and 2 or fewer of every other letters.
19. What is the most common answer in the set {2,3,5,7,11,13,15,19,23}
(A) A
(B) B
(C) C
(D) D
(E) E
Among other primes, there are two each of A, D, and E. All other answers must be solved first, then using the totals in questions 1-5, D and E must be eliminated.
20. How long is the longest sequence of consecutive questions which have the same answer?
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
A, B, and C contradicted by 13-16. E contradicted by 25.
21. Which is the last question to have the answer A?
(A) 20
(B) 21
(C) 22
(D) 23
(E) 24
A contradicts itself. B contradicts itself. D implies 23A which implies 24C which implies 23D, which is a contradiction. E contradicts 25.
22. Which is the last question to have the answer B?
(A) 25
(B) 24
(C) 23
(D) 22
(E) 21
From 21.
23. Which is the last question to have the answer C?
(A) 24
(B) 23
(C) 22
(D) 21
(E) 20
A contradicts 21. B contradicts itself. C contradicts itself. E contradicts 25.
24. Which is the last question to have the answer D?
(A) 21
(B) 22
(C) 23
(D) 24
(E) 25
23 rules out A, B, and C. 25 rules out E.
25. Which is the last question to have the answer E?
(A) 15
(B) 16
(C) 17
(D) 18
(E) 19
From 22.
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