SOLUTION: Credit cards companies use an algorithm for distinguising between valid credit card numbers and collections of random digits. The algorithm is as follows: 1. begin by doubling all

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Question 208428: Credit cards companies use an algorithm for distinguising between valid credit card numbers and collections of random digits. The algorithm is as follows:
1. begin by doubling all even-positioned digits when counting from right to left.
2. Determine the sum of the digits from the digits from step one and each of the unaffected (odd-positioned digits) digits in the original number.
3. Determine the number to be added to the sum from step two so that this new sum is a multiple of 10. This number is the check digit.
Using the algorithm, what should be the final digit of this credit card number?
601143871005123_
In the above process there are two sums you are finding: one involving the odd-positioned digits and the other involving the even-positioned digits that were doubled. first consider the sum of the odd-positioned digits. what is the most the sum could be affected by if an incorrect digit was entered? explain why this occurs.
next consider the even-positioned digits that were doubled. it is possible here to have numbers that result in double digits. recall how this sum is determine. how is it possible that a single digit error would be detected? (hint: i think i can make a table that shows possible values for the check digit, the double of the check digit and the resulting sums...i just don't know how)
Answer by Edwin McCravy(20054) (Show Source):
You can put this solution on YOUR website!
We can't tell what the even-positioned digits are when counting from
right to left, because we don't know whether to count the missing digit
on the right as digit #1 or the last one listed as #1. Please repost
making this clear.