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Puzzle 13
What belongs to you, but other people use it more than you?
Hint
You might find Pythagoras' theorem very useful [a2 + b2 = c2].
Answer
148 inches.
We can use Pythagoras' theorem if we draw an imaginary line across to create a right-angled triangle.
The hypotenuse is equal to the rope's length R. The bottom of the triangle is 48 inches. The vertical side is R − 8 (the difference between 20 inches and 12 inches).
Pythagoras' theorem tells us that:
a2 + b2 = c2
Where c is the hypotenuse.
This gives us:
482 + (R − 8)2 = R2
2304 + (R − 8)(R − 8) = R2
2304 + R2 − 16R + 64 = R2
2304 − 16R + 64 = 0
16R = 2368
R = 148
As required.
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Puzzle 16
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.
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
It is now four years since I first asked for support, and I would like to sincerely thank everyone who has helped me. BrainBashers doesn't show adverts, and I continue to depend on the ongoing support from everyone who enjoys the site.
