document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=465807>Question 465807</A>: <I><SPAN STYLE=\"word-break: break-all;\"> In the first 99 natural numbers, digit 4 comes how many times?\r<BR>\n" );
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document.write( "I got 4,14,24,34,40,41,42,43,44,45,46,47,48,49,54,64,74,84,94 (19 times)<BR>\n" );
document.write( "But the answer written in my book is 20 times.\r<BR>\n" );
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document.write( "Which number am i missing? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #319308 by </B><A HREF=/tutors/aboutme.mpl?userid=richard1234><B>richard1234(7193)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=richard1234><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=richard1234><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=319308\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 44 has two fours. There are 19 numbers, but 20 4's.\r<BR>\n" );
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document.write( "An easier way to count them is to list the numbers by unit digit and by tens digit, and always use the ellipsis (...) if necessary. You can organize them into sets like {4, 14, ...,94} and {40, 41, ..., 49}. Without writing every term you can easily count the number of elements by doing certain transformations like\r<BR>\n" );
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document.write( "{4, 14, ..., 94} --> {0, 1, ..., 9} (removed 4's) --> {1, 2, ..., 10} (added 1), 10 elements. </SPAN>\n" );
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