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Here is snippet of section A of the curious multiple-choice entrance exam into the exclusive BrainBashers puzzle club.

1. The first question with B as the correct answer is:

A. 1
B. 4
C. 3
D. 2

2. The answer to Question 4 is:

A. D
B. A
C. B
D. C

3. The answer to Question 1 is:

A. D
B. C
C. B
D. A

4. The number of questions which have D as the correct answer is:

A. 3
B. 2
C. 1
D. 0

5. The number of questions which have B as the correct answer is:
A. 0
B. 2
C. 3
D. 1

1. C
2. D
3. B
4. C
5. B

A nice, complicated, and sometimes confusing puzzle.

Step 1
Question 1 can't be A, as this would mean that Q1 was the first question with B as the answer and therefore contradict itself.

Q1 can't be B as this would mean Q4 was the first question with B as the answer, but Q1 would actually be the first question with B as the answer.

If we test Q1 as having answer C, you'll see that Q3 points back to Q1 correctly and is logically consistent. This is a possibility.

If we test Q1 as having answer D, then Q2's answer is B, which points to Q4's answer being A, which means that there are 3 questions with D as the answer. Which would mean that Q3 and Q5 were both D, but Q3 would have to be A, as we're testing that Q1 is D.

Step 2
Looking at Q4 (how many questions can have D as the answer), clearly it can't be D (zero), as this would contradict itself. It can't be A (three) as we only have 2 questions without an answer.

If Q4 was B, then the remaining questions (Q2 and Q5) would both be D, which would make Q2 point to Q4 having C as an answer, which contradicts our guess of Q4 being B.

So Q4 must be C.

Which means that Q2 has answer D.

Which means that Q5 has answer B (as no other option is allowed and we must have two questions with answer B). QED!

Back to the puzzles...

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