Logic time!

This may be an internut chestnet by now (I mean, an internet chestnut), but it was new to me. There is indeed a unique solution – but in order to get it you have to help yourself to that information, which is something I find mildly annoying in logic puzzles like nurikabe and such, but there it is. Hint: that an answer choice makes the thereby completed statement true is not sufficient reason to regard it as the correct answer (see #19 for an example!). Be careful! A mistake early on means that when you run into trouble you have to start over.

HT: A math teacher blog here (he's not sure what the ultimate source is - probably Lewis Carroll or some other joker). There's an inconclusive thread on the solution here. [Update 12/22: link fixed]

1. The first question whose answer is (B) is —
(A) 1 — (B) 2 — (C) 3 — (D) 4 — (E) 5

2. The only two consecutive questions with identical answers are —
(A) 6 & 7 — (B) 7 & 8 — (C) 8 & 9 — (D) 9 & 10 — (E) 10 & 11

3. The number of questions with answer (E) is —
(A) 0 — (B) 1 — (C) 2 — (D) 3 — (E) — 4

4. The number of questions with 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) temperature, wind velocity, latitude and longitude