1. What’s the next number in this sequence? 2,8,18,32,50, ___
3. The number 676 is a perfect square. As a mental exercise: What’s its square root?
6. A prime number has no factors except itself and one. How many prime numbers are there between the numbers 80 and 90?
9. The circumference of the Earth is approximately 40,000 kilometers, and someone has just made a metal band that circles the Earth, touching the ground at all locations.
You come along at night, as a practical joke, and add just 10 meters to its length (one hundredth of one kilometer !)
It is now one four-millionth longer, and sits magically just above the ground at all locations.
How far has it risen …
a. Could a flea squeeze under it?
b. Could a rabbit squeeze under it?
c. Could a man squeeze under it?
The distances between towns A & B, B & C, C & D and D & A are the same.
The red lines represent the main roads linking each town to the next, whereas the green line is a circular ring road which serves all five towns.
The courier has a choice of using the main roads at an average of 50 km / h, or the ring road at an average 60 km / h.
Assuming he stops at each town for the same period regardless of which road he uses, estimate (or guess) which of the two choices of road should be quicker: main roads or ring road?