document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1161225>Question 1161225</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A child wishes to build up a triangular piles of toy bricks so as to have one brick In the top flow, 2 in the second, 3 in the third and so on . if he has 100 bricks, how many rows can complete and how many bricks has he left </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #784725 by </B><A HREF=/tutors/aboutme.mpl?userid=ikleyn><B>ikleyn(52788)</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=784725\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> .<BR>\n" );
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document.write( "A triangular pile with n rows of bricks requires  1 + 2 + 3 + . . . + n = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28n%2A%28n%2B1%29%29%2F2 ALIGN=MIDDLE  ALT=\"%28n%2A%28n%2B1%29%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > bricks  (= the sum of the first n natural numbers).\r\n" );
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document.write( "The table is\r\n" );
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document.write( "n  (rows)    1   2   3    4     5     6     7     8     9    10    11   12   13\r\n" );
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document.write( "N (bricks)   1   3   6   10    15    21    28     36   45    55    66   78   91\r\n" );
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document.write( "So, having 100 bricks, the child can build 13-stores pyramid.\r\n" );
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document.write( "He (or she) will use 91 bricks, and 100-91 = 9  bricks will left.\r\n" );
document.write( "</PRE>\r<BR>\n" );
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document.write( "Solved.\r<BR>\n" );
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document.write( "If you want to know the basics for it, it is about arithmetic progressions.\r<BR>\n" );
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document.write( "For introductory lessons on arithmetic progressions see \r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;- <A  rel=nofollow HREF=http://www.algebra.com/algebra/homework/Sequences-and-series/Arithmetic-progressions.lesson>Arithmetic progressions</A>\r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;- <A  rel=nofollow HREF=http://www.algebra.com/algebra/homework/Sequences-and-series/The-proofs-of-the-formulas-for-arithmetic-progressions.lesson>The proofs of the formulas for arithmetic progressions</A> \r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;- <A  rel=nofollow HREF=http://www.algebra.com/algebra/homework/Sequences-and-series/Problems-on-arithmetic-progressions.lesson>Problems on arithmetic progressions</A>  \r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;- <A  rel=nofollow HREF=http://www.algebra.com/algebra/homework/Sequences-and-series/Word-problems-on-arithmetic-progressions.lesson>Word problems on arithmetic progressions</A> (*)\r<BR>\n" );
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document.write( "in this site.\r<BR>\n" );
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document.write( "By the way, you will find a picture for your problem in the lesson marked (*) in the list.\r<BR>\n" );
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document.write( "Also, &nbsp;you have this free of charge online textbook in ALGEBRA-II in this site\r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;- <A  rel=nofollow HREF=https://www.algebra.com/algebra/homework/complex/ALGEBRA-II-YOUR-ONLINE-TEXTBOOK.lesson>ALGEBRA-II - YOUR ONLINE TEXTBOOK</A>.\r<BR>\n" );
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document.write( "The referred lessons are the part of this online textbook under the topic <U>\"Arithmetic progressions\"</U>.\r<BR>\n" );
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document.write( "Save the link to this textbook together with its description\r<BR>\n" );
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document.write( "Free of charge online textbook in ALGEBRA-II<BR>\n" );
document.write( "https://www.algebra.com/algebra/homework/complex/ALGEBRA-II-YOUR-ONLINE-TEXTBOOK.lesson\r<BR>\n" );
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document.write( "into your archive and use when it is needed.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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