WHY DOES 0! =1 ?

Many of us are confused why 0! =1. This is the best explanation that I have came across.

If you have 3 playing cards in your hand, you can arrange them in 3! different ways. In other words you can put them in 3 x 2 x 1 = 6 different orders.
If you have 2 cards, you can put them in 2! different ways which is 2.
If you just have 1 card you can only arrange it 1! ways which is 1.
But if you have ZERO cards then there's also one way of doing that!

The BEAR HUNTER Puzzle

A bear hunter sets out from camp and walks one mile south.
He sees a bear and is about to shoot it.
The bear grabs his gun and eats it.
The hunter runs away one mile east.
He then walks one mile north and gets back to his camp and changes his underwear.
What colour was the bear?
This is a classic puzzle, because it looks like the hunter has moved like this: 
...and it doesn't tell you what colour the bear is!

However there IS somewhere on Earth where it is possible for him to move south, east then north and get back again!

Perfect Numbers

What is a perfect number?

A perfect number is a whole number, an integer greater than zero; and
when you add up all of the factors less than that number, you get that number.

Examples:

The factors of 6 are 1, 2, 3 and 6.1 + 2 + 3 = 6

The factors of 28 are 1, 2, 4, 7, 14 and 28.1 + 2 + 4 + 7 + 14 = 28

The factors of 496 are 1, 2, 4, 8, 16, 31, 62, 124, 248 and 496.1 + 2 + 4 + 8 + 16 + 31 + 62 + 124 + 248 = 496

The factors of 8128 are 1, 2, 4, 8, 16, 32, 64, 127, 254, 508, 1016, 2032, 4064 and 8128. I'll let you add them up.

How to tell a number whether it is divided by 11.

Here's how to tell when a number up to 1,000 divides exactly by 11.
If it's a 2 digit number, the digits will be the same. (E.g.33 or 77)
If it's a 3 digit number: add the two outside digits and take away the middle digit. If the answer is 0 or 11 then the number will divide by 11. Examples: 451: 4+1-5 =0 so 451 will divide by 11. 869: 8+9-6=11 so 869 will divide by 11.