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Hint: You might find Pythagoras' theorem very useful [a^{2} + b^{2} = c^{2}].
Answer: 148 inches.
We can use Pythagoras' theorem if we draw an imaginary line across to create a rightangled 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:
a^{2} + b^{2} = c^{2}
Where c is the hypotenuse.
This gives us:
48^{2} + (R  8)^{2} = R^{2}
^{ }^{ } 2304 + (R  8)(R  8) = R^{2}
^{ } 2304 + R^{2}  16R + 64 = R^{2}
^{ }^{ } 2304  16R + 64 = 0
^{ }^{ } 16R = 2368
^{ }^{ } R = 148
As required.
Puzzle 454
Can you tell what this rebus is?
GLOOOOKD
[Ref: ZHRO]
Hint: Say what you see.
Answer: Looking good.
LOOK in the word GOOD.
Puzzle 455
Place letters into the grid such that every row, column, and 2x2 block has letters (in any order) that form a common word.
Each letter is only used once, and no letter is repeated in the rows/cols/blocks.
Across: DUCK, PLUM, TOES, BALE
Down : DOME, PLUS, CUBE, TALK
Boxes : DUMP, LUCK, SOLE, BEAT
Note : Other anagrams of these words are OK as long as they don't change the answer grid.
Puzzle 456
The BrainBashers mechanical computer is a very sensitive device, it consists of interlocked toothed gear cogs.
The largest cog has 168 teeth and the others have 49, 32 and 15 respectively.
By accident, Daniel started to rotate the largest cog.
How many revolutions must he rotate the largest cog make before the computer is back in its starting position with all of the cogs where they started?
Hint: Try breaking each cog size into prime factors.
Answer: 140 revolutions.
If we break each wheel into its prime factors, we get:
168= 2 x 2 x 2 x 3 x 7
49 = 7 x 7
32 = 2 x 2 x 2 x 2 x 2
15 = 3 x 5
So
revolutions x 168

2 x 2 x 2 x 2 x 2 x 3 x 5 x 7 x 7
revolutions x 2 x 2 x 2 x 3 x 7

2 x 2 x 2 x 2 x 2 x 3 x 5 x 7 x 7
revolutions

2 x 2 x 5 x 7
revolutions

140
Which means revolutions = 140.
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