Reasoning
If we convert the question to algebra, we have:
((n^2 + 4) x 2 − 3) x 4 − n = 20
Expanding the brackets and simplifying gives:
(2n^2 + 8 − 3) x 4 − n = 20
(2n^2 + 5) x 4 − n = 20
8n^2 + 20 − n = 20
8n^2 − n = 0 (*)
8n − 1 = 0
8n = 1
n = 1/8
In the equation marked (*) zero is also a potential solution, but as the question tells us that we "Start with a number larger than 0" we know that n can't be 0, and therefore we can safely divide by n.
Hint
Light travels over 186,000 miles each second.
Answer
Miles travelled by light in a second.
Reasoning
Light travels over 186,000 miles per second.
There are 2.54cm in an inch, 12 inches in a foot, 3 feet in a yard, and 1760 yards in a mile. So there are 2.54 x 12 x 3 x 1760 = 160,934.4cm in a mile.
??
Puzzle 372
Traffic was bad going to work this morning. I only managed to average 30 mph.
How fast must I go home tonight, along the same route, to average 60 mph for the entire round trip?
Hint
It doesn't matter what the distance is, so try a random distance.
Answer
This cannot be done.
It does not matter how far the trip is, let's assume that it is random distance, say 60 miles, and remembering that Time = Distance ÷ Speed.
The morning trip took 60 miles ÷ 30 mph = 2 hours.
To average the required 60 mph, we would have to travel the total distance (of 120 miles) in 2 hours. However, we've already used all of the two hours for the morning trip!
Choosing any random distance would also show that it can't be done.
