document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1210184>Question 1210184</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I can only remember a seven-digit telephone number if the first three digits (the \"prefix\") are equal to the next three digits or the last three digits. For example, I can remember 389-3892 and 274-9274.\r<BR>\n" );
document.write( "\n" );
document.write( "How many seven-digit telephone numbers can I remember?\r<BR>\n" );
document.write( "\n" );
document.write( "(For this problem, a telephone number cannot start with a 0.)<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #851502 by </B><A HREF=/tutors/aboutme.mpl?userid=ikleyn><B>ikleyn(52781)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ikleyn><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=ikleyn><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=851502\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> .<BR>\n" );
document.write( "I can only remember a seven-digit telephone number if the first three digits (the \"prefix\") <BR>\n" );
document.write( "are equal to the next three digits or the last three digits. <BR>\n" );
document.write( "For example, I can remember 389-3892 and 274-9274.\r<BR>\n" );
document.write( "\n" );
document.write( "How many seven-digit telephone numbers can I remember?\r<BR>\n" );
document.write( "\n" );
document.write( "(For this problem, a telephone number cannot start with a 0.)<BR>\n" );
document.write( "~~~~~~~~~~~~~~~~~~~~~~~~~~\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Counting in the post by @CPhill is &nbsp;INCORRECT.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "It becomes incorrect, when CPhill starts consider the overlapping case.<BR>\n" );
document.write( "Namely, he suddenly considers then the 9-digit telephone numbers instead of 7-digit numbers.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "In reality, the overlapping case may really have place.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "It happens when in the form  ABC-XABC part XAB is the same as ABC.\r<BR>\n" );
document.write( "\n" );
document.write( "But it happens if and only if  A=X, B=A, C = B, i.e.  A = B = C.\r<BR>\n" );
document.write( "\n" );
document.write( "The number of such cases (overlapping) is 9  (not 900, as @CPhill counts them).\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Therefore, the final answer in the problem is  9000 + 9000 - 9 = 18000-9 = 17991.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<U>ANSWER</U>.  You can remember 17991 telephone numbers.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Solved correctly.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );