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so for this week's assignment we're actually using something known as the loons check algorithm so loon Hanz loon from IBM developed this algorithm back in 1950 1954 to basically validate credit cards validate cards I'll just shorthand that and we can prove this we can look at it and there's a valid credit card look my camera zoom and focus on that don't worry it is empty but we're going to go ahead and use this card to sort of prove the lewin algorithm so I'm going to just write it out here for a second for a to skip ahead I got to write three five two nine eight nine two six three zero four nine four so how does the lewin check work one of the things that we have to do is we have to think about how we're presenting our numbers these aren't just kind of this is it a math I'm not separating things by commas it's not a numerical value it we think about it in at least programming as more of a string and so if we looked at the position of these cards we actually start counting at zero and that means if I keep counting up 1 2 3 4 5 6 7 8 9 8 10 11 12 13 14 15 okay so we've laid them out from 0 to 15 even though there are 16 digits I know so what we can do with this is we can do something first known as the sum of odd places I just counted out a bunch of numbers everywhere I have an odd number I'm going to add that now one of the things I do have to point out is I'm going to go right to left I know that may not seem like a big deal when we're dealing with say visa however if we're looking at different cars like Mastercard or American Express or Discover this actually sort of matters so I'm going to start and I'm going to start counting from yeah from sort of my 15 slot 4 plus 0 plus 6 plus 9 plus 9 plus 5 plus 7 plus 8 plus 7 plus 8 so all I do is I add these together I'll just add them so 4 + 0 is 4 but a 4 and a 6 is going to produce a 10 10 and 9 produces 19 9 + 9 or 19 and 9 produces 28 28 33 40 48 so by adding all these not these odd placed numbers I get 48 all right simple nothing too terribly crazy going on there but what about those even spots I haven't done anything with those well let me go ahead and just write them out first 9 3 2 8 2 3 4 4 now I purposely did not put the plus sign in between them and there's a good reason for it because one of the things I'm going to have to do is I'm actually going to have to double every number that's not just it sure for something like 4 right here I can double it and that's going to be fun same with this one I can double this one however I'm going to come back over here to this 9 when I double this number I get an 18 make that a little bit more obvious I get an 18 I don't add the 18 however what I do is I actually break it down and I say well I'm going to add one and I'm going to add eight at eight again this is going to produce on nine I know that seems odd now gonna put it down here in a different color just to kind of keep it in track I produce a nine well I do the same algorithm I double the three this gives me a 6 the 6 is perfectly fine the six is not a double-digit so I can just go ahead and add that to my equation I can do the exact same thing with the two I double the two I get a four I add the 4 however when I get to this 18 I double be 18 and I get a 16 or i double the 8 and I get a 16 I do the exact same thing I did with a 9 I'm going to have to add the 1 and the 6 so 1 plus 6 equals 7 I keep going luckily all three are all four of these numbers can get doubled without having to kind of run through that second part of four six eight eight four six eight eight so if I take those numbers and I'm going to move them a little up here so it's a little easier for us to see so 9 plus 6 that produces 15 15 plus 4 that produces 19 19 plus 7 it's 26 26 plus 4 equals 30 trying to avoid my head as you can imagine 30 plus 6 equals 36 36 plus 8 is going to equal 44 and 44 plus 8 equals 52 okay so why does any of this matter I'm going to delete a few things now that I've taken all this math I'm just going to write that out I'm going to state now that I've got the sum of odd places in the sum of even places 52 if I take these two numbers and I add them together I get 100 now the Loon check basically says that if when I won these two songs if I sum the odds and I sum the evens using the double approach if the number that I get is divisible by 10 I have a valid card let's say for example I didn't have a valid card because we just you know yes we prove that this is the valid card if however I changed let's say for example this four had been a five well everything would have been completely off my odd digits would have been 49 I would have added that together I would have produced 101 and let me actually do this instead I would have went 101 modulus 10 and when I check to see if it was divisible by zero this is not true thus it would have been an in valid card