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The Barg's Self-Referential Logic Puzzle - Medium

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], and [D].
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 submittedNovember 7, 2023
Times taken28
Average score60.0%
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1. Which question is the first to have A as the correct answer?
(A) 1 ✓
(B) 2 ✓
(C) 3 ✓
(D) 4 ✓
2, 3, and 4 are all ruled out by not having A as their answer.
2. Which question is the first to have B as the correct answer?
(A) 1 ✓
(B) 2 ✓
(C) 3 ✓
(D) 4 ✓
13 and 15 imply that [D] = 6, and without 2 the maximum value of [D] would be 5.
3. Which question is the last to have C as the correct answer?
(A) 12 ✓
(B) 13 ✓
(C) 14 ✓
(D) 15 ✓
See 15.
4. Which question is the last to have D as the correct answer?
(A) 12 ✓
(B) 13 ✓
(C) 14 ✓
(D) 15 ✓
15 rules out C and D. See 13.
5. Which is the first pair of questions to share the same answer?
(A) 4 and 5 ✓
(B) 3 and 4 ✓
(C) 2 and 3 ✓
(D) 1 and 2 ✓
See 10.
6. What is the answer to question 12?
(A) D ✓
(B) B ✓
(C) C ✓
(D) A ✓
7. [D] = ?
(A) [A] ✓
(B) [B] ✓
(C) [C] ✓
(D) None of the above ✓
13 and 15 imply that [D] = 6, and without 7 the maximum value of [D] would be 5.
8. How many unique letters exist in the answers to perfect square questions?
(A) 1 ✓
(B) 2 ✓
(C) 3 ✓
(D) 4 ✓
D is impossible, C is ruled out by 15, and A is ruled out by 1 and 4 not having the same answer.
9. [B] = ?
(A) 6 ✓
(B) 4 ✓
(C) 2 ✓
(D) 0 ✓
A is ruled out by 7, C is ruled out by 15, and D is ruled out by 2.
10. How many unique letters exist in the answers to the first three questions?
(A) 0 ✓
(B) 1 ✓
(C) 2 ✓
(D) 3 ✓
A is impossible. 11 tells us that this answer must be the same answer as 5. 5B and 10B contradict each other, as do 5D and 10D.
11. Which of the following sets all share the same answer?
(A) Prime numbers ✓
(B) Even numbers ✓
(C) Multiples of 3 ✓
(D) Multiples of 5 ✓
This is the first step. A is wrong because it would imply 2 and 3 would also be A, which would mean 5 cannot be A. 6 and 12 being nonequivalent rule out B and C.
12. What is the answer to question 6?
(A) D ✓
(B) C ✓
(C) B ✓
(D) A ✓
15 implies that 6 and 12 must be A and D, but the order is fixed only after 9 implies 14B.
13. [D] - [C] = ?
(A) 6 ✓
(B) 5 ✓
(C) 4 ✓
(D) 3 ✓
By 15, [C] = 3. The maximum value of [D] after evaluating questions 11, 5, 10, 15, and 3 is 6: at most one of 1 and 2, 3, exactly one of 6 and 12, 7, 11, 13. Thus [D] - [C] is at most 3.
14. What is the answer to question 12?
(A) D ✓
(B) A ✓
(C) B ✓
(D) C ✓
C is ruled out by 15, and D is ruled out by 4C (indirectly by 15). B is implied by 9 (there are no other places for the fourth B to go).
15. [C] = ?
(A) 1 ✓
(B) 2 ✓
(C) 3 ✓
(D) 4 ✓
11 tells us that 5, 10, and 15 must share an answer. See 10 for why this answer is C. Thus, C is ruled out of every question that is not 5, 10, or 15.
1 Comments
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mightythor
+3
Level 66
Nov 9, 2023
Nice job. Took me an hour+, I think. 20 min. b4 bed with a spreadsheet to get the first few, and then another session to finish. Long enough that it's not easy, but not so long as to want to give up.
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