document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1150894>Question 1150894</A>: <I><SPAN STYLE=\"word-break: break-all;\"> We call a number a descending number if each digit is strictly smaller than the digit that comes  before it. For example, 863 is a descending number. How many 3-digit descending numbers are there? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #772464 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=772464\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"times\" color=\"black\" size=\"3\"><BR>\n" );
document.write( "If 2 is in the hundreds place, then there is only 1 three-digit number that is a descending number and it is 210.\r<BR>\n" );
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document.write( "If 3 is in the hundreds place, then there are three such descending numbers<BR>\n" );
document.write( "310<BR>\n" );
document.write( "320<BR>\n" );
document.write( "321\r<BR>\n" );
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document.write( "If 4 is in the hundreds place, then we have six descending numbers<BR>\n" );
document.write( "410<BR>\n" );
document.write( "420<BR>\n" );
document.write( "421<BR>\n" );
document.write( "430<BR>\n" );
document.write( "431<BR>\n" );
document.write( "432\r<BR>\n" );
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document.write( "If 5 is in the hundreds place, then we have ten descending numbers<BR>\n" );
document.write( "510<BR>\n" );
document.write( "520<BR>\n" );
document.write( "521<BR>\n" );
document.write( "530<BR>\n" );
document.write( "531<BR>\n" );
document.write( "532<BR>\n" );
document.write( "540<BR>\n" );
document.write( "541<BR>\n" );
document.write( "542<BR>\n" );
document.write( "543\r<BR>\n" );
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document.write( "The counts so far are: 1, 3, 6, 10\r<BR>\n" );
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document.write( "The jump from 1 to 3 is +2<BR>\n" );
document.write( "The jump from 3 to 6 is +3<BR>\n" );
document.write( "The jump from 6 to 10 is +4\r<BR>\n" );
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document.write( "This pattern continues because we have 15 descending numbers if 6 is the hundreds digit<BR>\n" );
document.write( "610<BR>\n" );
document.write( "620<BR>\n" );
document.write( "621<BR>\n" );
document.write( "630<BR>\n" );
document.write( "631<BR>\n" );
document.write( "632<BR>\n" );
document.write( "640<BR>\n" );
document.write( "641<BR>\n" );
document.write( "642<BR>\n" );
document.write( "643<BR>\n" );
document.write( "650<BR>\n" );
document.write( "651<BR>\n" );
document.write( "652<BR>\n" );
document.write( "653<BR>\n" );
document.write( "654\r<BR>\n" );
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document.write( "And there are 15+6 = 21 descending numbers with 7 as the hundreds digit, 21+7 = 28 descending numbers with 8 as the hundreds digit, and finally 28+8 = 36 descending numbers with 9 as the hundreds digit.\r<BR>\n" );
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document.write( "The counts are<BR>\n" );
document.write( "1,3,6,10,15,21,28,36<BR>\n" );
document.write( "Add them up<BR>\n" );
document.write( "1+3+6+10+15+21+28+36 = 120\r<BR>\n" );
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document.write( "Answer: <font color=red size=4>120</font>\r<BR>\n" );
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document.write( "Below is a pastebin link of all 120 three-digit descending numbers<BR>\n" );
document.write( "<a  rel=nofollow HREF= \"https://pastebin.com/WqFYtfc4\">https://pastebin.com/WqFYtfc4</a><BR>\n" );
document.write( "This is to avoid adding further clutter to this current page.<BR>\n" );
document.write( "</font> </SPAN>\n" );
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