# Self-Referential Aptitude Test

## by Jim Propp (propp@math.mit.edu)

A few years ago I wrote a "Self-Referential Aptitude Test" as part of
a longer chain of puzzles. Since this puzzle seems to have taken on a
life of its own and has been spreading around various parts of the
'net, I figure I might as well post it to silent-tristero before
someone else does. Feel free to pass it on (with attribution).

The solution to the puzzle is unique, and in some cases the knowledge
that the solution is unique can actually give you a short-cut to
finding the answer to a particular question, but it's possible to find
the unique solution even without making use of the fact that the
solution is unique. (Thanks to Andy Latto for bringing this subtlety
to my attention.)

I should mention that if you don't agree with me about the answer to
#20, you will get a different solution to the puzzle than the one I
had in mind. But I should also mention that if you don't agree with
me about the answer to #20, you are just plain wrong. :-)

Jim Propp

### S.R.A.T.

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 the answer E is
- (A)
- 0
- (B)
- 1
- (C)
- 2
- (D)
- 3
- (E)
- 4

4. The number of questions with the 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 the above
- (E)
- all of the above

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)
- an even number
- (B)
- an odd number
- (C)
- a perfect square
- (D)
- a 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 the above
- (E)
- all of the above

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 the above

19. The answer to this question is
- (A)
- A
- (B)
- B
- (C)
- C
- (D)
- D
- (E)
- E

20. Standardized test : intelligence :: barometer :
- (A)
- temperature (only)
- (B)
- wind-velocity (only)
- (C)
- latitude (only)
- (D)
- longitude (only)
- (E)
- all of the above