document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=257912>Question 257912</A>: <I><SPAN STYLE=\"word-break: break-all;\"> What is the sum of all the digits of all the positive integers that are less than 100? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #189781 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=189781\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the positive digits are 1 through 9.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "0 is a non-negative digits.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "0 is not a positive digit.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "when we sum up the digits it won't matter if we include 0 or not because the sum of all 0's is still 0.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "when you count to 100, you have 1 set of tens digits and 1 set of units digits.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the total set of digits is shown in the following table:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<PRE STYLE=\"white-space: pre-wrap; white-space: -moz-pre-wrap; white-space: -pre-wrap; white-space: -o-pre-wrap; word-wrap: break-word;\">\r\n" );
document.write( "00 10 20 30 40 50 60 70 80 90\r\n" );
document.write( "01 11 21 31 41 51 61 71 81 91\r\n" );
document.write( "02 12 22 32 42 52 62 72 82 92\r\n" );
document.write( "03 13 23 33 43 53 63 73 83 93\r\n" );
document.write( "04 14 24 34 44 54 64 74 84 94\r\n" );
document.write( "05 15 25 35 45 55 65 75 85 95\r\n" );
document.write( "06 16 26 36 46 56 66 76 86 96\r\n" );
document.write( "07 17 27 37 47 57 67 77 87 97\r\n" );
document.write( "08 18 28 38 48 58 68 78 88 98\r\n" );
document.write( "09 19 29 39 49 59 69 79 89 99\r\n" );
document.write( "</PRE><BR>\n" );
document.write( "the ones digits are on the right of each number.<BR>\n" );
document.write( "the tens digits are on the left of each number.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "example:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "number 49:<BR>\n" );
document.write( "9 is the ones digit<BR>\n" );
document.write( "4 is the tens digit\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "to sum up all the digits, we sum up all the ones digits and all the tens digits separately and then add them together.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "within each column, the ones digits add up to 45.   that would be the sum of 1 through 9.   \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "within each column, the tens digits add up to 10 * the digit shown.   that would be 10 * 1, 10 * 2, etc.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "you get the following number:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<PRE STYLE=\"white-space: pre-wrap; white-space: -moz-pre-wrap; white-space: -pre-wrap; white-space: -o-pre-wrap; word-wrap: break-word;\">\r\n" );
document.write( "                     sum of tens digit     sum of units digit    total\r\n" );
document.write( "from 0 to 9                  0                   45                45\r\n" );
document.write( "from 10 to 19               10                   45                55\r\n" );
document.write( "from 20 to 29               20                   45                65\r\n" );
document.write( "from 30 to 39               30                   45                75\r\n" );
document.write( "from 40 to 49               40                   45                85\r\n" );
document.write( "from 50 to 59               50                   45                95\r\n" );
document.write( "from 60 to 69               60                   45               105\r\n" );
document.write( "from 70 to 79               70                   45               115\r\n" );
document.write( "from 80 to 89               80                   45               125\r\n" );
document.write( "from 90 to 99               90                   45               135\r\n" );
document.write( "  \r\n" );
document.write( "total                      450                  450               900\r\n" );
document.write( "</PRE>\r<BR>\n" );
document.write( "\n" );
document.write( "sume of all the positive digits less than 100 is equal to 900.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );