document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1091573>Question 1091573</A>: <I><SPAN STYLE=\"word-break: break-all;\"> An empty box with top, bottom and four sides, is a two and a half-foot cube. It is completely filled with smaller boxes that each measure ten inches on each side.\r<BR>\n" );
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document.write( "How many small boxes will be on the top layer in the big box?	<BR>\n" );
document.write( "How many small boxes will be touching the four sides of the big box?	<BR>\n" );
document.write( "How many small boxes are not against the top, bottom, or any side of the big box?	<BR>\n" );
document.write( "How many small boxes are on the bottom and also touching the sides of the big box?	<BR>\n" );
document.write( "How many small boxes are on the top and also touching two sides of the big box? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #706018 by </B><A HREF=/tutors/aboutme.mpl?userid=KMST><B>KMST(5328)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=KMST><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=KMST><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=706018\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The big empty box is shaped like a cube with edges'lengths measuring<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%261%2F2 ALIGN=MIDDLE  ALT=\"2%261%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=feet=2.5feet=2.5%2A12inches=30inches ALIGN=MIDDLE  ALT=\"feet=2.5feet=2.5%2A12inches=30inches\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The easy way to calculate answers is to visualize how the box looks,<BR>\n" );
document.write( "and how it could be filled.<BR>\n" );
document.write( "You would start by covering the bottom of the big box with one layer of small boxes.<BR>\n" );
document.write( "After that you would add more layers, one by one, until the box is full.<BR>\n" );
document.write( "For each layer, you would start by putting<BR>\n" );
document.write( "as many small boxes in a row as would fit against one of the cube's edges.<BR>\n" );
document.write( "The number of boxes in a row would be<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=30inches%2F%2210+inches%22=3 ALIGN=MIDDLE  ALT=\"30inches%2F%2210+inches%22=3\"   DISABLED_style= \"max-width:90%; height:auto;\" > small boxes.<BR>\n" );
document.write( " <BR>\n" );
document.write( "How many small boxes will be on the TOP LAYER in the big box?	<BR>\n" );
document.write( "With <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3 ALIGN=MIDDLE  ALT=\"3\"   DISABLED_style= \"max-width:90%; height:auto;\" > boxes against each edge,<BR>\n" );
document.write( "each layer would have <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2A3=9 ALIGN=MIDDLE  ALT=\"3%2A3=9\"   DISABLED_style= \"max-width:90%; height:auto;\" > small boxes,<BR>\n" );
document.write( "so there would be <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%289%29 ALIGN=MIDDLE  ALT=\"highlight%289%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > small boxes on the top layer<BR>\n" );
document.write( "(and on each and every layer).<BR>\n" );
document.write( "There would also be <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3 ALIGN=MIDDLE  ALT=\"3\"   DISABLED_style= \"max-width:90%; height:auto;\" > layers filling the big box, for a total of<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2A3%2A3=3%5E3=27 ALIGN=MIDDLE  ALT=\"3%2A3%2A3=3%5E3=27\"   DISABLED_style= \"max-width:90%; height:auto;\" > small boxes.<BR>\n" );
document.write( " <BR>\n" );
document.write( "How many small boxes will be TOUCHING THE FOUR SIDES of the big box?	<BR>\n" );
document.write( "Each layer would be a 3 by 3 square small box arrangement,<BR>\n" );
document.write( "with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1 ALIGN=MIDDLE  ALT=\"1\"   DISABLED_style= \"max-width:90%; height:auto;\" > small box at the center,<BR>\n" );
document.write( "surrounded by the remaining small boxes around the layers' edges.<BR>\n" );
document.write( "in each layer, that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1 ALIGN=MIDDLE  ALT=\"1\"   DISABLED_style= \"max-width:90%; height:auto;\" > small box at the center would be the only one<BR>\n" );
document.write( "not touching any sides.<BR>\n" );
document.write( "The remaining <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9-1=8 ALIGN=MIDDLE  ALT=\"9-1=8\"   DISABLED_style= \"max-width:90%; height:auto;\" > small boxes in each layer, <BR>\n" );
document.write( "for a total of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2A8=highlight%2824%29 ALIGN=MIDDLE  ALT=\"3%2A8=highlight%2824%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > small boxes<BR>\n" );
document.write( "will be touching at least one side of the big box.<BR>\n" );
document.write( "None could be touching all four sides, though.<BR>\n" );
document.write( " <BR>\n" );
document.write( "How many small boxes are NOT AGAINST THE TOP, BOTTOM OR ANY SIDE of the big box?	<BR>\n" );
document.write( "We have found that there would be <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3 ALIGN=MIDDLE  ALT=\"3\"   DISABLED_style= \"max-width:90%; height:auto;\" > layers of small boxes,<BR>\n" );
document.write( "each one consisting of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9 ALIGN=MIDDLE  ALT=\"9\"   DISABLED_style= \"max-width:90%; height:auto;\" > small boxes,<BR>\n" );
document.write( "with one of them as the top layer.<BR>\n" );
document.write( "Of course, another one of the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3 ALIGN=MIDDLE  ALT=\"3\"   DISABLED_style= \"max-width:90%; height:auto;\" > layers would be the bottom layer,<BR>\n" );
document.write( "so every one of the small boxes in those two layers<BR>\n" );
document.write( "would be against the top or bottom of the big box.<BR>\n" );
document.write( "The middle layer, would have <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9 ALIGN=MIDDLE  ALT=\"9\"   DISABLED_style= \"max-width:90%; height:auto;\" > small boxes that would not be<BR>\n" );
document.write( "against the top or bottom of the big box.<BR>\n" );
document.write( "However, the small boxes on each edge of that 3 by 3 square small box arrangement<BR>\n" );
document.write( "would be against a side of the big box,<BR>\n" );
document.write( "and that accounts for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8 ALIGN=MIDDLE  ALT=\"8\"   DISABLED_style= \"max-width:90%; height:auto;\" > of those <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9 ALIGN=MIDDLE  ALT=\"9\"   DISABLED_style= \"max-width:90%; height:auto;\" > small boxes.<BR>\n" );
document.write( "Only the other <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%281%29 ALIGN=MIDDLE  ALT=\"highlight%281%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > small box at the center of the middle layer<BR>\n" );
document.write( "would be not against the top, bottom, or any side of the big box.\r<BR>\n" );
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document.write( "How many small boxes are ON THE BOTTOM AND ALSO TOUCHING THE SIDES of the big box?<BR>\n" );
document.write( "As stated above,<BR>\n" );
document.write( "exactly <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%288%29 ALIGN=MIDDLE  ALT=\"highlight%288%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > small boxes on each layer (including the bottom layer)<BR>\n" );
document.write( "are touching the sides of the big box.<BR>\n" );
document.write( " 	<BR>\n" );
document.write( "How many small boxes are ON THE TOP AND ALSO TOUCHING TWO SIDES of the big box?<BR>\n" );
document.write( "As stated above, each layer would be a 3 by 3 square small box arrangement,<BR>\n" );
document.write( "with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1 ALIGN=MIDDLE  ALT=\"1\"   DISABLED_style= \"max-width:90%; height:auto;\" > small box at the center,<BR>\n" );
document.write( "surrounded by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8 ALIGN=MIDDLE  ALT=\"8\"   DISABLED_style= \"max-width:90%; height:auto;\" > small boxes around the layers' edges.<BR>\n" );
document.write( "Of the small boxes in each layer (including the top layer),<BR>\n" );
document.write( "only the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%284%29 ALIGN=MIDDLE  ALT=\"highlight%284%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > small boxes on the corners<BR>\n" );
document.write( "are touching TWO sides of the big box. </SPAN>\n" );
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