**Entry Exam Section A** - Logic Puzzles

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

Q1. The first question with B as the correct answer is:

A. Q1

B. Q4

C. Q3

D. Q2

Q2. The answer to Q4 is:

A. D

B. A

C. B

D. C

Q3. The answer to Q1 is:

A. D

B. C

C. B

D. A

Q4. The number of questions that have D as the correct answer is:

A. 3

B. 2

C. 1

D. 0

Q5. The number of questions that have B as the correct answer is:

A. 0

B. 2

C. 3

D. 1

Puzzle Copyright © Kevin Stone

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Hint

Can Q1 have A as its answer?

Answer

Q1. C – the first question with B as the correct answer is Q3.

Q2. D – the answer to Question 4 is C.

Q3. B – the answer to Question 1 is C.

Q4. C – the number of questions that have D as the correct answer is one.

Q5. B – the number of questions that have B as the correct answer is two.

Reasoning

A complicated, and sometimes, confusing answer!

Can Q1 be A? No, because this would tell us that Q1 was the first question with B as the answer, which would be a contradiction (as we've just assumed Q1 was A).

Can Q1 be B? No, because this would tell us that Q4 was the first question with B as the answer, which would be a contradiction (as we've just assumed it was Q1).

Can Q1 be C? Possibly, because Q3 points back to Q1 correctly, and is logically consistent.

Can Q1 be D? No, because:

Q2 would be B

Q4 would be A – which means that we have three questions with D

which means that Q3 would have to be D, and this would tell us that Q1 is A, which would be a contradiction (as we've just assumed that Q1 is D).

Therefore, **Q1 is C**, which means that **Q3 is B**.

We can ignore Q2 for a moment, as it asks us about Q4, and look at Q4 first.

Looking at Q4 (how many questions have D as the answer) it can't be D (zero), as this would contradict itself.

It can't be A (three) as we only have two other questions without an answer.

If Q4 was B, then the remaining questions (Q2 and Q5) would both have to be D, and:

Q5 being D would mean that only one question was B, which would be a contradiction (as Q3 is already B, and we've just assumed that Q4 is also B).

So **Q4 must be C**, which means that **Q2 is D**.

Looking at Q5, it can't be A (as Q3 is B), it can't be D (as Q4 tells us that we only have one question with D as the answer – Q2). It can't be C as we don't have three questions that are B. So **Q5 is B** (the two questions are Q3 and Q5).