Coke Rewards

I've collected the codes attached to Coca Cola products for awhile now. I'm about ready to give that up for several reasons. For one, I probably don't need to give up hours recording those codes to finally have enough to get items such as a free t-shirt advertising their company. Anyway, those codes seem longer than they need to be. Here is one I recently used - 5KBMNOMN6FWPFW. There doesn't seem to be a reason for it. I figure the possible combinations are astronomical. There doesn't seem to be anything in particular that would limit the possibilities. For example, I thought maybe the first entry might always be a digit. No, sometimes a digit and sometimes a letter. They do state that the letter O (oh) and the number 0 (zero) are registered the same. This is also true entering the letter I and the number 1.

I had given this some, but not a lot of thought previously. But I read on their website's FAQ section the following:

Why did My Coke Rewards change from 12 digit codes to 14 digit codes? 

Due to the popularity of our program, we’ve made the transition from 12 digit codes to 14 digit codes, to ensure we have a steady supply of codes for you, our loyal members. Please note that 12 digit codes are ineligible effective 8/1/2014.

Really? Twelve are not enough? How many is that anyway? Without knowing of any other limiting factors I assume there are 34 possibilities for the first part of the code. (The 26 letters of the alphabet, the 10 numeric digits, and throwing out the two repeats.) So how many for the 12 digit codes?

                      34x34x34x34x34x34x34x34x34x34x34x34 = 2.386x10^18

I understand there are about 8 billion people on the Earth currently. Dividing those two numbers we see there are enough codes that each person on Earth could have 2,983,000,000 of them. Seems like enough. But apparently there was a need to go to a fourteen digit code. (Since Coke uses the term "digit" to designate both numbers and letters, I will too.)

Students can brush up on their scientific notation a little more by finding the amount of 14 digit codes.
   
                           2.386x10^18 x 34 x 34  = 2.758x10^21

I looked on-line and found that scientists have a rough estimate of grains of sand of all the beaches of the world. There very roughly, 7.5x10^18 grains of sand in the world. Hopefully 14 digits are going to be enough for the Coke folks.