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.
Hint
Try to find out where Mrs Umbrella lives first.
Answer
From, left to right:
#1 Mrs Scott - glass
#2 Mrs Umbrella - straw
#3 Mr Tidsley - brick
#4 Mr Wilshaw - wood
Reasoning
If we separate and label the clues, and label the bungalows #1, #2, #3, #4 from left to right we can see that: Mrs Scott's bungalow is somewhere to the left of the wooden one.The third one along is brick.Mrs Umbrella owns a straw bungalowMr Tidsley does not live at either end.Mr Tidsley lives somewhere to the right of the glass bungalow.Mr Wilshaw lives in the fourth bungalow.The first bungalow is not made from straw.
By (6) Mr Wilshaw lives in the fourth bungalow.
#1
#2
#3
#4 Mr Wilshaw
By (3), Mrs Umbrella owns the straw bungalow. By (7) it isn't #1, by (2) it isn't #3, so it must be #2.
#1
#2 Mrs Umbrella - straw
#3
#4 Mr Wilshaw
By (4), Mr Tidsley must therefore live in #3, which, by (2) is the brick bungalow.
#1
#2 Mrs Umbrella - straw
#3 Mr Tidsley - brick
#4 Mr Wilshaw
By (1), Mrs Scott's bungalow must be #1, and #4 must be the wooden one.
#1 Mrs Scott
#2 Mrs Umbrella - straw
#3 Mr Tidsley - brick
#4 Mr Wilshaw - wood
This leaves #1 as the glass bungalow.
#1 Mrs Scott - glass
#2 Mrs Umbrella - straw
#3 Mr Tidsley - brick
#4 Mr Wilshaw - wood
Reasoning
If we convert the question to algebra, we have:
((n^2 + 4) x 2 − 3) x 4 − n = 20
Expanding the brackets and simplifying gives:
(2n^2 + 8 − 3) x 4 − n = 20
(2n^2 + 5) x 4 − n = 20
8n^2 + 20 − n = 20
8n^2 − n = 0 (*)
8n − 1 = 0
8n = 1
n = 1/8
In the equation marked (*) zero is also a potential solution, but as the question tells us that we "Start with a number larger than 0" we know that n can't be 0, and therefore we can safely divide by n.
