# Self-referential IQ test

SELF-REFERENTIAL APTITUDE TEST, by Jim Propp (propp@math.wisc.edu)
The solution to the following puzzle is unique; in some cases the
knowledge that the solution is unique may 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.  🙂
You may now begin work.
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
(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 is to intelligence as barometer is to
(A) temperature (only)
(B) wind-velocity (only)
(C) latitude (only)
(D) longitude (only)
(E) temperature, wind-velocity, latitude, and longitude
( to go to the main SRAT page, go to jamespropp.org/srat.html )

Note: The following IQ test has been reproduced exactly from this site.

This is an amazing test!

Also see Terry Tao’s site for more puzzles.

Start of test.

SELF-REFERENTIAL APTITUDE TEST, by Jim Propp (propp@math.wisc.edu)

The solution to the following puzzle is unique; in some cases the

knowledge that the solution is unique may 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.  🙂

You may now begin work.

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

(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 is to intelligence as barometer is to

(A) temperature (only)

(B) wind-velocity (only)

(C) latitude (only)

(D) longitude (only)

(E) temperature, wind-velocity, latitude, and longitude

( to go to the main SRAT page, go to jamespropp.org/srat.html )

The End.