Puzzle 57
In Farmer Donald's hay loft there are a number of ants, mice and chickens.
There are ten times as many ants as there are mice, and there are four times as many mice as there are chickens.
Altogether there are 1,806 feet.
How many chickens are there?
Puzzle Copyright © Kevin Stone
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Hint
Think about the number of legs.
Answer
There are 7 chickens, 28 mice and 280 ants.
Reasoning
For every chicken (2 legs) we have 4 mice (16 legs) and 40 ants (240 legs) = 258 legs.
So we can divide the total number of legs by 258, giving 1,806 ÷ 258 = 7 (chickens).
Puzzle 58
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.
Puzzle 59
HWAYETRDETIPZLHV
OMNLTESOSHSUZEAE
Puzzle Copyright © Kevin Stone
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Hint
The question is written in English, but not in its usual order.
Answer
32.
Reading one letter from the top row and then one from the bottom row, the puzzle reads: 'How many letters does this puzzle have'.
Puzzle 60
What number comes next in the sequence:
11 · 13 · 17 · 31 · 37 · 71 · 73 · 79 · 97 · ?
Puzzle Copyright © Kevin Stone
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Hint
A very tricky puzzle involving prime numbers.
Answer
101.
These are prime numbers, which, when reversed, are also prime.
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