How many ways can you arrange 10 books?

If you have 3 books, how many ways can you arrange them? 6 ways...there are 3 choices for  the first book, two choices for the second book leaving the last book to be the third one.  3 x 2 x 1= 6..this is also known as 3!  pronounced "3 factorial" as opposed to THREE!!
ABC
ACB
BAC
BCA
CAB
CBA

If you have 4 books, there are now 4! or 24 different ways to arrange these books.

Whats amazing is if you have 10 books, the number of possible arrangements is 10! or
10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x  1 which is 3,628,800

April 2013 Brain Teaser Solution

Q:Which unit fractions 1/2, 1/3, 1/4 etc have terminating decimals and which repeat? For example, 1/2 = 0.5 terminates but 1/3 = .3333etc and repeats.

How many unit fractions up to 1/1000 have terminating decimals?  What is the key to figuring this out?

A:  28
The first handful of fractions that terminate starting with 1/2 are:

1/2 = .5, 1/4 = .25, 1/8 = .125, 1/10 = .1

Notice the denominators are all composed of 2s and 5s

For example 4 = 2 x 2 and 8 = 2 x 2 x 2 and 10 = 2 x 5

This works becuase our number system is base 10 and base 10 is easy to express fractions as decimals if the factors of the denominator are 2s and/or 5s.

Here is a list of numbers that have 2 and/or 5 as their only factors:

2 4 5 8 10 16 

20 25 32 40 50 

64 80 100 125 128

160 200 250 256 320

400 500 512 625 640
800 1000

Is Utility the Only Reason for Math? Math vs The Odyssey

http://www.theatlantic.com/business/archive/2013/04/heres-how-little-math-americans-actually-use-at-work/275260/

Here's How Little Math Americans Actually Use at Work

Less than a quarter of employees do any calculations more complicated than basic fractions, and blue-collar workers generally do more advanced math than their white-collar friends.

and how many people use "The Odyssey" at work?