A Simple Self-Referential Test

Question

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

Original PDF source: http://mrhonner.com/wp-content/uploads/2012/05/Simple-Self-Referential-Test-2.pdf

• 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
    

Answer 1

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

Answer 2

Obvious ones:

3 and 10 have answers B and D, one each. Anything else leads to contradiction.
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.

Answer 3

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.

Answer 4

The answer sequence is
1.E 2.A 3.B 4.A 5.C 6.A 7.B 8.B 9.E 10.D

As mentioned in those previous comments some answers are pretty straight forward and especially 9th one as the 8th questions option leads all to the same option 'E' of the 9th question.That means options A+E must be equal to 5 as 10 is not possible. So we take A=3,E=2,B=3,C=1,D=1.All other relations can be deduced logically easily.To solve this start from the last question as it is a loop.If you do that rest would be easy.Cheers!