At last BrainBashers horse derby, 10 fine horses completed the gruelling 3 mile course. Predictably, as per every year, the results mysteriously went missing. However, various marshals remembered the following snippets of information:
Simple Simon lost to Zebra Wings.
Zebra Wings beat Simple Simon, Frogman's Flippers and Apple Pie.
Fizzy Pop lost to Minty Mouth, Simple Simon and CD Player.
Frogman's Flippers beat Windy Hill, CD Player and Simple Simon.
Top Hat lost to CD Player, Kippers and Apple Pie.
CD Player beat Top Hat and Fizzy Pop.
Apple Pie lost to Zebra Wings and Simple Simon.
Kippers lost to Apple Pie and Frogman's Flippers.
Frogman's Flippers beat Fizzy Pop, Minty Mouth and CD Player.
CD Player lost to Frogman's Flippers, Kippers and Apple Pie.
Hint: These are the first letters of the words: A, C, D, D, I, L, M, N, P, R.
acq + uit + tal = acquittal
con + duc + tor = conductor
dec + kch + air = deckchair
dif + fer + ent = different
imp + ort + ant = important
lig + htn + ing = lightning
myt + hol + ogy = mythology
new + sag + ent = newsagent
pol + ice + man = policeman
rec + tan + gle = rectangle
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