# A Simple Self-Referential Test

You can play it online here: https://www.brainzilla.com/logic/self-referential-quiz/simple-srq-2/

• Each test has some number of multiple choice questions about itself;
• There is only one correct answer for each question;
1. The answer to this question is

A.  A
B.  B
C.  C
D.  D
E.  E

2. The number of questions whose answer is A is equal to the number of questions whose answer is

A.  B
B.  C
C.  D
D.  E
E.  All of the above

3. The answer to number 10 is

A.  E
B.  D
C.  C
D.  B
E.  A

4. The answer to question 6 is

A.  A
B.  B
C.  C
D.  D
E.  E

5. The answer to this question is the same as the answer to number

A.  3
B.  4
C.  5
D.  6
E.  7

6. The first question whose answer is B is

A.  3
B.  4
C.  5
D.  6
E.  7

7. The number of questions whose answer is C is

A.  0
B.  1
C.  2
D.  3
E.  4

8. The answer to this question is how many letters away from the answer to the next question?

A.  4
B.  3
C.  2
D.  1
E.  0

9. The number of questions whose answer is a vowel is

A.  An even number
B.  An odd number
C.  A prime number
D.  A perfect square
E.  A multiple of 5

10. The answer to number 3 is

A.  C
B.  D
C.  A
D.  B
E.  E

• It's unsolvable ATM. – Nautilus Apr 18 '17 at 10:30
• How about changing "A prime number" to "An odd prime number"? – Nautilus Apr 18 '17 at 12:47
• @ Nautilus - it isn't broken because of that. Question 9 in accepted answer can be only A. If it was B or D it would make answer to 2 wrong while C and E would be wrong by itself. Consider 1 - it can be answered anything. So, the clause obviously can refer only to "there must be a single answer and a single option that makes the table valid". Say there is one other C (and no other conditions) => 7 B and C would be both valid = solution is invalid as there is no unique answer to 7. It is broken because there is no unique solution and it is marked as "logical-deduction". – Zizy Archer Apr 19 '17 at 8:21
• @ABcDexter Similarity in construction and concept is not sufficient to close as duplicate (or we'd have eliminated all the "Use operations and these digits to make this value" questions long ago). – Rubio Apr 8 '18 at 18:46
• @Rubio Ok, understood. – ABcDexter Apr 8 '18 at 18:53

After some deducing and trial and error, I got this as a complete test:

1. The answer to this question is

A. A
B. B
C. C
D. D
E. E

2. The number of questions whose answer is A is equal to the number of questions whose answer is

A. B
B. C
C. D
D. E
E. All of the above

3. The answer to number 10 is

A. E
B. D
C. C
D. B
E. A

4. The answer to question 6 is

A. A
B. B
C. C
D. D
E. E

5. The answer to this question is the same as the answer to number

A. 3
B. 4
C. 5
D. 6
E. 7

6. The first question whose answer is B is

A. 3
B. 4
C. 5
D. 6
E. 7

7. The number of questions whose answer is C is

A. 0
B. 1
C. 2
D. 3
E. 4

8. The answer to this question is how many letters away from the answer to the next question?

A. 4
B. 3
C. 2
D. 1
E. 0

9. The number of questions whose answer is a vowel is

A. An even number
B. An odd number
C. A prime number
D. A perfect square
E. A multiple of 5

10. The answer to number 3 is

A. C
B. D
C. A
D. B
E. E

So a few of them are fairly straight forward. This is the path I took.

5 is obviously its own answer.
3 and 10 only have one possibility to match itself up.
4 and 6 allow themselves to be paired and solved with some deduction.
I chose to make 1, A because it would allow 9 to be A and then that easily gives you 8's answer
It then filled itself out mostly as 7 could be D which then made 2, C

• What exactly does question 8 mean? – greenturtle3141 Apr 17 '17 at 20:00
• @greenturtle3141 example: the letter F is 5 away from the letter A in sequential order of the alphabet – indubitablee Apr 17 '17 at 20:30
• Re: Q9 - 2 is an even prime. – Nautilus Apr 18 '17 at 10:24
• @n_palum how does 3 and 10 have only one possibility to match up, B and D are interchangeable. – Sikorski Apr 18 '17 at 11:07
• I don't think you can start with Question 5 being C-it only happens to be the case to solve the rest of the questions. C will always be a correct answer but it is not necessarily the only correct answer (like question 1). – jousle Apr 18 '17 at 17:08

Obvious ones:

5 cannot have A or D as answer.
6 precludes 1 and 2 to have answer B. It cannot have answer C or D.
This means 4 can have A, B or E as answer.
And that number of A needs to be equal to B, D or E. 8 leads to 9 being answered by A (8 is C), C (8 is D) or E (any case of 8).
Answer E on 9 means 5 are A or E, 10 is impossible due to questions 3 and 10. C leads to 2, 3, 5 or 7, while A leads to 2, 4, 6 or 8.

Now some other eliminations and considerations:

2 cannot have E as answer. This would lead to 2x all letters, meaning 9 needs to be answered A (4 A or E). 7 would have to be answered C and 3 and 10 have B and D. 4 and 6 double letters, meaning at least one letter would end up appearing 3x, which is a contradiction.
5 cannot be E. If it was, 7 would have to be E, and there aren't enough possible answers C left for it to be.

This leads us to the following options:

 1: A, C, D, E
2: A, C, D
3: B, D * opposite of 10
4: A, B, E * same as 6
5: B, C
6: A, B, E * same as 4
7: A, B, C, D, E
8: A, B, C, D, E
9: A, C, E
10: B, D * opposite of 3


Now I don't see a way to progress further without guessing:

One option I see is: 5B (chosen to eliminate as many options as possible). It leads to 3D, 4B, 6B, 10B. Now another guess: 1A, 2A, 7A, 8A, 9E would be a possible solution.

As this answer is different and also valid, the question does not have unique solution.

A9 being "A" means that the number of "answer is vowel" is: i) even; ii) not 2 (because 2 is prime); iii) not 4 (because 4 is a perfect square); iv) not 8,10,12,etc. So the number of "answer is vowel" must be 6. From 10 answers, deducting 4 answers (A3, A10, A9 and A8), 6 remain. Of these 6, 5 must be "answer is vowel" because A9 is already "answer is vowel". Meaning that only one is "answer is not vowel". And that leads to no solution.