Puzzle 141
Entry Exam Section B - Logic Puzzles
Here is a snippet of section B of the curious multiple-choice entrance exam into the exclusive BrainBashers puzzle club.
Q1. The answer to Q2 is:
A. B
B. A
C. D
D. C
Q2. The answer to Q3 is:
A. C
B. D
C. B
D. A
Q3. The answer to Q4 is:
A. D
B. A
C. C
D. B
Q4. The answer to Q1 is:
A. D
B. C
C. A
D. B
Puzzle Copyright © Kevin Stone
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Hint
Can Q1's answer be A?
Answers
1. D
2. C
3. B
4. A
Reasoning
The easiest way to solve this puzzle is to use Q1 to check the logic.
If Q1's answer was A, this tells us that Q2's answer is B, which tells us Q3's is D, which tells us Q4's answer is B, which tells us Q1's answer is C. A contradiction.
If Q1's answer was B, this tells us that Q2's answer is A, which tells us Q3's is C, which tells us Q4's answer is C, which tells us Q1's answer is A. A contradiction.
If Q1's answer was C, this tells us that Q2's answer is D, which tells us Q3's is A, which tells us Q4's answer is D, which tells us Q1's answer is B. A contradiction.
If Q1's answer was D, this tells us that Q2's answer is C, which tells us Q3's is B, which tells us Q4's answer is A, which tells us Q1's answer is D. Which is correct, and therefore the correct answer.
Puzzle 142
Disastrous Dave was washing windows on a multi-storey office building when he took a fall off a fifty foot ladder, directly onto the concrete pavement below.
Amazingly, Dave didn't get hurt at all.
How can this be possible?
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Hint
Where was Dave standing when he fell?
Answer
Dave fell off the very bottom rung of the ladder!
Puzzle 143
During a recent expedition, three intrepid adventurers were left stranded in the middle of the desert with only a crate full of apples.
During the night, Alex woke up and decided to hide some of the apples and hid a third, then promptly fell asleep again.
Billie woke up shortly after and also decided to hide a third of the remaining apples and then also dozed back to sleep.
Finally, Charlie woke up and seeing the others were asleep, took a third of what was left.
Of course, none of the adventurers knew of the other's antics, so, in the morning, they shared the remaining apples, each receiving sixteen. How many apples were in the crate originally?
Puzzle Copyright © Kevin Stone
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Hint
How many apples were left after Charlie had taken some?
Answer
162 apples.
Alex hid 54, leaving 108.
Billie then hid 36, leaving 72.
Charlie then hid 24, leaving 48 available to share in the morning.
Reasoning
To work these numbers out, we start at the end and work backwards.
At the end there were 16 apples each, therefore there were 48 apples in total.
Charlie removed one third leaving 48, so there must have been 72 apples before.
Billie removed one third leaving 72, so there must have been 108 apples before.
Alex removed one third leaving 108, so there must have been 162 apples before.
Puzzle 144
At the local BrainBashers Sunday School meeting, the teacher brought in some puppies.
There were 20 more children than puppies.
In the corner of the room, within the ant's nest, the number of ants was 10 times the number of children.
In total, including the teacher, the children, the puppies, and the ants, there were 1440 legs in the room.
How many children attended?
Puzzle Copyright © Kevin Stone
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Hint
Work out the total number of legs.
Answer
23 children (46 legs).
With 230 ants (1380 legs), 3 puppies (12 legs), and 1 teacher (2 legs).
If we call the number of puppies P, then there were (P + 20) children and 10 x (P + 20) ants, and a single teacher. If we now count the legs, we get:
Puppies:
P x 4 = 4P
Children:
(P + 20) x 2 = 2P + 40
Ants:
10 x (P + 20) x 6 = 60P + 1200
Teacher: 2
A total of 66P + 1242
Giving:
66P + 1242 = 1440
66P = 198
P = 3
So there were 3 puppies, hence 23 children.
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