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ok today we're going to take a look at validating credit cards and also we're going to look at the number of possible credit cards that a company can issue and this goes back to our too many numbers unit when we did it with zip codes we also did it with social security numbers so here we're going to do it with credit cards now first thing you want to do is put out all your possible positions of the credit card now but one thing we learn in this unit does credit card has 16 digits so each digit we want to choice out there possibilities now 16 is a very large number so what we're going to do is we're going to we're going to use a little scientific notation to express our answer otherwise this number is just going to be too big to handle so lay out your 16 digits okay and I put them in groups of 4 to kind of help us stay organized and let's take a look at the first two digits now I just made these numbers up I know that these are cards duendes are in a 4 but I'm not quite sure what the options are but let's just say it's either a 4 6 of 4 7 or 4 8 that basically just gives the for your options are only one and the other the next digit you have exactly 3 choices so that's going to be a 3 now the remaining digits are all 10 and I'm not going to write all these you could but it really gets old so that's going to go all the way not quite to the end because it does have a check digit number okay and the check digit number is determined by all the numbers preceding it so you really only have one choice at the end for that so we couldn't be just any number here is a special nominee for determining on how all the the numbers added up so that's only one choice so how many have a power of 10 so we got 1 times 3 times 1 so it's just 3 times 10 to how many digits well it was 16 we used up three digits okay so that leaves 13 digits that have 10 choices so we're going to put that to the power of 13 so 3 times 10 to the 13 cards be issued okay so this is not really too difficult just map out your all your positions and the possibilities for each position and just remember the best last digit can only be one choice as well and just use exponents for the base 10 because that's going to be your largest one and that should cover that type of question now I'm going to move it up and the more difficult the more challenging questions are validating a credit card or finding a check digit to make it valid remember again the sum must end in zero okay and let's just look at these directions that they give you okay you got to add the digits in odd number positions and double this total then add the number of odd position digits that are more than four to the total that means you actually have to count that I'll show you an example of that then add to even position digits and then choose and check a digit number that will make its final sum and in zero so those are the steps what I've done here is sort of kind of condensed them and summarized steps and so we can stay a little bit more organized so the first step is to add the odd position digits so I'm going to underline all the odd position digits would be the first the third the fifth and so on so it's every other one from there these are all the odd position digits that have been underlined in red so we want to add up four plus two plus zero plus one plus four plus eight plus zero you don't really have to add these zeros I just don't want to anybody lose track there so you should add all that up and you should get 20 and then it says times two so you want to double that when they say double that amount it's times two with equal 40 so we're starting down this step at 40 now we must add the number of odd positions greater than four it's the odd positions great enforce and look at the all the underlined which how many are greater than four well that one's not greater than four it's equal to not to not zero not four eight that's 1 so I'm going to put a little arrow so we can or account just put a little count of the number greater than four it looks like there's only one so here we're just going to add one because there's only one odd position value that is greater than four so you have 41 here now you want to add to that add the even digits so what are the even digits they are 1 plus 8 plus 0 plus two plus three plus nine plus one and those are the even and of course the check digit number will be an even number as well when you add all that up you should get 24 so it's 41 plus 24 and you end up with 65 and sis your total 65 you want a number that will make it end in zero so the next number is 70 so choose D to equal 5 so 65 plus 5 will equal 70 so it ends in zero and there you have it so again the credit cards a little bit more challenging than the UPC codes it's just got a few more steps and you've got to stay organized so hopefully that method helps you you can come up with your own method of course but staying organized is going to be the hardest part about getting these ones correct so I hope that helps and if you have any questions feel free to um mention them in the comments below thanks for watching