Puzzle 121
This year, Farmer Stone's harvest of apples was quite significant.
He decided to donate some of the apples to the local community, 1,672 people in all.
Every person aged 50 or more received 16 apples, and every person under 50 received 96 apples.
Only 3/4 of the over 50s collected their apples, and only 1/8 of the under 50s collected theirs.
How many apples did the farmer give away?
Puzzle Copyright © Kevin Stone
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Hint
Try a random number of over 50s to see what happens.
Answer
20,064 apples.
Reasoning
It doesn't matter how old the people are.
As only 3/4 of the over 50s claimed 16 apples, this averages out to 12 apples each.
Similarly, only 1/8 of the under 50s claimed 96 apples, this again averages out to be 12 apples each.
Therefore, the total number of apples was 1,672 x 12 = 20,064.
Puzzle 122
What is the 20th prime number?
2, 3, 5, 7, …
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2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, …
Answer
71.
The first twenty prime numbers are: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71.
Puzzle 123
A trout's tail weighs eight pounds.
Its head weighs as much as the tail and one-half of the body combined, and the body weighs as much as the head and tail combined.
What does the whole trout weigh?
Puzzle Copyright © Kevin Stone
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Hint
A little bit of algebra might help.
Answer
64 pounds.
The head weighs 24 pounds, the body weighs 32 pounds, and the tail weighs 8 pounds.
Reasoning
The trout is made up of the head, body and tail, H, B and T.
We are told that:
T = 8
(1) H = T + B ÷ 2
(2) B = H + T
Placing T into (1) and (2) we get:
(3) H = 8 + B ÷ 2
(4) B = H + 8
Using (4) in (3) we get:
H = 8 + B ÷ 2
(5) H = 8 + (H + 8) ÷ 2
Multiplying (5) by 2 we get:
2H = 16 + H + 8
2H = 24 + H
H = 24
Therefore, by (2):
B = H + T
B = 24 + 8
B = 32
Giving:
H = 24
B = 32
T = 8
And a total of 24 + 32 + 8 = 64 pounds.
Puzzle 124
Four shepherds were watching over their flocks, and they were commenting on how many sheep they each had.
If Alex had three more sheep, then he'd have one fewer sheep than Billie.
Whereas Drew has the same number as the other three shepherds put together.
If Charlie had three fewer sheep, he'd have exactly three times the number of Alex.
If they were evenly distributed, they'd each have eleven sheep.
How many sheep does Alex have?
Puzzle Copyright © Kevin Stone
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Hint
Find how many sheep Drew has first.
Answer
3.
Reasoning
If we denote Alex by A, Billie by B, Charlie by C, and Drew by D and number the clues.
If Alex had three more sheep, then he'd have one fewer sheep than Billie.
Whereas Drew has the same number as the other three shepherds put together.
If Charlie had three fewer sheep, he'd have exactly three times the number of Alex.
If they were evenly distributed, they'd each have eleven sheep.
By (4):
A + B + C + D = 44
And, by (2), these are shared equally between A + B + C and D.
So D = 22, and A + B + C = 22 (*)
By (1):
A + 3 = B – 1
A + 4 = B
By (3):
C – 3 = 3A
C = 3A + 3
Substitute B and C in (*):
A + (A+4) + (3A+3) = 22
5A + 7 = 22
5A = 15
A = 3
And, B = 7, C = 12.
Double-Checking
A = 3, B = 7, C = 12, D = 22.
(1) 3 + 3 = 7 – 1
(2) 3 + 7 + 12 = 22
(3) 12 – 3 = 3 x 3
(4) 3 + 7 + 12 + 22 = 44, and 44 ÷ 4 = 11 each.
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