Here is a snippet of section D of the curious multiple-choice entrance exam into the exclusive BrainBashers puzzle club.
Q1. Which is the first question where c) is the correct answer?
a) Q3
b) Q4
c) Q1
d) Q2
Q2. Which is the first question where a) is the correct answer?
a) Q4
b) Q2
c) Q3
d) Q1
Q3. Which is the first question where d) is the correct answer?
a) Q1
b) Q2
c) Q4
d) Q3
Q4. Which is the first question where b) is the correct answer?
Reasoning
Let's look at Q1 first, and check each possible option:
If Q1's answer was a):
… we'll leave checking this for now, because …
If Q1's answer was b):
… we'll leave checking this for now, because …
If Q1's answer was c):
it would reference itself, and we'd learn nothing new, and we'd then have to check Q2.
So, let's start with Q2 first instead of Q1.
If Q2's answer was a):
an immediate contradiction, as Q4 can't be the first answer with a) as we've assumed Q2's answer is a).
If Q2's answer was b):
an immediate contradiction, as Q2 can't be the first answer with a) as we've assumed Q2's answer is b).
If Q2's answer was c):
Q3's answer would be a)
Q1's answer would be d)
confirming Q2's answer as c)
leaving Q4's only possible answer as b)
no contradiction.
If Q2's answer was d):
Q1's answer would be a) (*)
Q3's answer would be c)
Q4's answer would be d)
Q1's answer would be b)
but this contradicts the section marked (*).
Therefore, the only possible answer with no contradiction is when Q2's answer is c).
We can then follow Q2's answer, which leads to the answers to Q1 to Q3. Q4 must then reference itself.
