document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1182202>Question 1182202</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Determine the number of three figures numbers between 100 and 999 inclusive, have only two consecutive figures identical. (I don't really understand this question.) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #812294 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13200)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=812294\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "Perhaps part of your problem in understanding the problem is that the vocabulary and grammar are both poor....<br><BR>\n" );
document.write( "Determine the number of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cross%28three%29 ALIGN=MIDDLE  ALT=\"cross%28three%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cross%28figures%29 ALIGN=MIDDLE  ALT=\"cross%28figures%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=red%28three-digit%29 ALIGN=MIDDLE  ALT=\"red%28three-digit%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > numbers between 100 and 999 inclusive <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=red%28that%29 ALIGN=MIDDLE  ALT=\"red%28that%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > have only two consecutive <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cross%28figures%29 ALIGN=MIDDLE  ALT=\"cross%28figures%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=red%28digits%29 ALIGN=MIDDLE  ALT=\"red%28digits%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > identical.<br><BR>\n" );
document.write( "Note also that \"between 100 and 999 inclusive\" is redundant, since it repeats the requirement that we are looking at only 3-digit numbers.<br><BR>\n" );
document.write( "There are two kinds of 3-digit numbers that have only two consecutive digits the same: AAB and ABB.<br><BR>\n" );
document.write( "(1) AAB (first two digits the same)<br><BR>\n" );
document.write( "The first digit can be any of 9 digits (it can't be 0): 9 choices<BR>\n" );
document.write( "The second digit has to be the same as the first: 1 choice<BR>\n" );
document.write( "The third digit has to be different from the first two; and it can be 0: 9 choices<br><BR>\n" );
document.write( "Number of 2-digit numbers of the form AAB: 9*1*9 = 81  (multiply the numbers of choices for each digit)<br><BR>\n" );
document.write( "(2) ABB (last two digits the same)<br><BR>\n" );
document.write( "The first digit can be any of 9 digits (it can't be 0): 9 choices<BR>\n" );
document.write( "The second digit has to be different from the first; and it can be 0: 9 choices<BR>\n" );
document.write( "The third digit has to be the same as the second: 1 choice<br><BR>\n" );
document.write( "Number of 2-digit numbers of the form AAB: 9*9*1 = 81<br><BR>\n" );
document.write( "ANSWER: The number of 3-digit numbers with only two consecutive digits the same is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cross%2881%2B81%2B162%29 ALIGN=MIDDLE  ALT=\"cross%2881%2B81%2B162%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > 81+81=162<br><BR>\n" );
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document.write( "Thanks to tutor @ikleyn for catching the typo in my answer.<br><BR>\n" );
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