The map below shows the street locations of a city. Position three police officers such that the entire length of every street can be seen by at least one officer.
After visiting one of my very old relatives, I travelled home in their old jalopy. The car was old and battered, it had a leak from the petrol tank, and I was stuck in second gear.
This meant that I could only travel along at a steady 30 miles per hour and managed a paltry 20 miles per gallon of fuel.
At the start of the journey, I had placed exactly 10 gallons of fuel into the tank. I knew though, that the fuel tank lost fuel at the rate of half a gallon per hour.
Just as I arrived home, the car stopped because it had run out of fuel and I had only just made it.
How far was it from my relative's house to my home?
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 180
Below, 10 nine-letter words have been broken into chunks of three letters.
The chunks have been moved around, no chunk is used twice, and all of the chunks are used.
Can you determine what the 10 words are?
som one dbr pen rtm ber
nes ent ive eph eti ens
mes off eak eid sep win
erd tel day ter wed tem
aft apa own car ern oon
Hint
The first letters of the words are: W, E, S, A, S, C, O, T, W, A.
Answers
Windbreak, eiderdown, sometimes, afternoon, September, carpenter, offensive, telephone, Wednesday, apartment.
win + dbr + eak = windbreak
eid + erd + own = eiderdown
som + eti + mes = sometimes
aft + ern + oon = afternoon
sep + tem + ber = september
car + pen + ter = carpenter
off + ens + ive = offensive
tel + eph + one = telephone
wed + nes + day = wednesday
apa + rtm + ent = apartment
