Problem:

This question forms a three question multiple choice test. After each question, there are 4 choices, each preceded by a letter. Please write down your answer as the ordered triple (letter of the answer of Question $\# 1$, letter of the answer of Question $\# 2$, letter of the answer of Question \#3). If you find that all such ordered triples are logically impossible, then write "no answer" as your answer. If you find more than one possible set of answers, then provide all ordered triples as your answer.
When we refer to "the correct answer to Question $X$ " it is the actual answer, not the letter, to which we refer. When we refer to "the letter of the correct answer to question $X$ " it is the letter contained in parentheses that precedes the answer to which we refer.
You are given the following condition: No two correct answers to questions on the test may have the same letter.

Question 1. If a fourth question were added to this test, and if the letter of its correct answer were (C), then:
(A) This test would have no logically possible set of answers.
(B) This test would have one logically possible set of answers.
(C) This test would have more than one logically possible set of answers.
(D) This test would have more than one logically possible set of answers.

Question 2. If the answer to Question 2 were "Letter (D)" and if Question 1 were not on this multiple-choice test (still keeping Questions 2 and 3 on the test), then the letter of the answer to Question 3 would be:
(A) Letter (B)
(B) Letter (C)
(C) Letter (D)
(D) Letter (A)

Question 3. Let $P_{1}=1$. Let $P_{2}=3$. For all $i>2$, define $P_{i}=P_{i-1} P_{i-2}-P_{i-2}$. Which is a factor of $P_{2002}$ ?
(A) 3
(B) 4
(C) 7
(D) 9