document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=208428>Question 208428</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Credit cards companies use an algorithm for distinguising between valid credit card numbers and collections of random digits. The algorithm is as follows:<BR>\n" );
document.write( "1. begin by doubling all even-positioned digits when counting from right to left.<BR>\n" );
document.write( "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.<BR>\n" );
document.write( "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.<BR>\n" );
document.write( "Using the algorithm, what should be the final digit of this credit card number?<BR>\n" );
document.write( "601143871005123_\r<BR>\n" );
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document.write( "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.\r<BR>\n" );
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document.write( "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) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #157682 by </B><A HREF=/tutors/aboutme.mpl?userid=Edwin+McCravy><B>Edwin McCravy(20055)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Edwin+McCravy><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=Edwin+McCravy><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=157682\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> We can't tell what the even-positioned digits are when counting from<BR>\n" );
document.write( "right to left, because we don't know whether to count the missing digit<BR>\n" );
document.write( "on the right as digit #1 or the last one listed as #1. Please repost <BR>\n" );
document.write( "making this clear.\r<BR>\n" );
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