In the early 1970's, Canada Post started using six-character postal codes. Each postal code uses three letters and three digits in an alternating pattern. How many different Canadian postal codes are possible?

A Canadian postal code looks like this:

K1A 3B1.

So you have: letter - digit - letter - digit - letter - digit.

The question doesn't say anything about restrictions on

which letters can be used, or restrictions on repeating letters

or digits within one postal code. So as far as we know, each

letter can be any one of 26, and each digit can be any one of 10.

The total number of possibilities would be

(26·10·26) · (10·26·10) = 17,576,000.

In the real world, though, (or at least in Canada), Postal codes

don't include the letters D, F, I, O, Q or U, and the first letter

does not use W or Z. When you work it out with these restrictions,

it means there's a theoretical limit of 7.2 million postal codes.

The practical limit is a bit lower, as Canada Post reserves some

codes for special functions, such as for test or promotional purposes.

One example is the code H0H 0H0 for Santa Claus! Other special

codes are for sorting mail bound for destinations outside Canada.

At the present time, there are a little over 830,000 active postal codes.

That's about 12% of the total possibilities, so there are still plenty of codes

left for expansion.