From: James Edward Gray II <james@...>
Date: 2007-04-29T13:22:57+09:00
Subject: Re: Checking Credit Cards (#122)

On Apr 28, 2007, at 10:50 PM, Phrogz wrote:

> On Apr 28, 9:04 pm, Ari Brown <a...@aribrown.com> wrote:
>> On Apr 27, 2007, at 7:59 AM, Ruby Quiz wrote:
>>>    1. Starting with the next to last digit and continuing with every
>>> other
>>>       digit going back to the beginning of the card, double the  
>>> digit
>>>    2. Sum all doubled and untouched digits in the number
>>>    3. If that total is a multiple of 10, the number is valid
>>
>>> For example, given the card number 4408 0412 3456 7893:
>>
>>>    Step 1:  8 4 0 8 0 4 2 2 6 4 10 6 14 8 18 3
>>>    Step 2:  8+4+0+8+0+4+2+2+6+4+1+0+6+1+4+8+1+8+3 = 70
>>>    Step 3:  70 % 10 == 0
>>
>>> Thus that card is valid.
>>
>> Uh, this is probably just affecting me but....
>>
>> In his example, after he doubles the second to last digit (call it
>> d), he uses mod10 on it (9*2 = 18 %10 = 8). That is the way to get
>> his numbers, but a) where does he say that and b) where do the 10 and
>> 14 come from?
>
> The confusing part (that I didn't catch when I read it) is that step 2
> is to sum all the *digits*, not the numbers.
>
> So
> step 1) 9 * 2 = 18
> step 2) 1 + 8
>
> He's not modding the result of the multiplication by 10, but rather
> adding up the resulting component digits. The same occurs with the 10
> and 14 (which Philip pointed out are the result of 5*2 and 7*2,
> respectively).

Yes, most descriptions tell you to mod 10 the bigger numbers to get  
the back to a single digit, but that adds a step that doesn't have  
any affect.  I left it out.

James Edward Gray II