The initial letters from the nursery rhyme, Hickory Dickory Dock.
Hickory, dickory, dock,
The mouse ran up the clock,
The clock struck one,
The mouse ran down,
Hickory, dickory, dock.
?
Puzzle 2
Last week, I travelled from Birmingham to Glasgow, the long way round (on a bicycle!).
On the first day, I travelled one quarter of the distance.
On day two, I travelled one half of the remaining distance.
On day three, I travelled three quarters of the remaining distance.
Yesterday I travelled one third of the remaining distance.
I now have 21 miles left to travel.
How far is it from Birmingham to Glasgow in total?
Hint
There are more than 37, look at the different sizes.
Answer
There are 64 hexagon-type shapes in total.
Reasoning
37 single hexagons
+ 19 hexagons that contain 7 smaller hexagons
+ 7 hexagons that contain 19 smaller hexagons
+ 1 large hexagon that contains all of the smaller hexagons.
??
Puzzle 4
A rope swing hangs vertically down so that the end is 12 inches from the ground, and 48 inches from the tree.
If the swing is pulled across so that it touches the tree, it is 20 inches from the ground.
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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