document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=331949>Question 331949</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A wooden cube whose edges are 4 inches is painted green.The cube is then cut into<BR>\n" );
document.write( "64 one-inch cubes. How many small cubes have exactly 1 green face? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #237937 by </B><A HREF=/tutors/aboutme.mpl?userid=galactus><B>galactus(183)</B></A><img src=\"/images/stars/stars-09.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=galactus><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=galactus><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=237937\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The number of one side paintings on an nxnxn cube is \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6%28n-2%29%5E2 ALIGN=MIDDLE  ALT=\"6%28n-2%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "In this case, we are told that n=4. So we have:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6%284-2%29%5E2=24 ALIGN=MIDDLE  ALT=\"6%284-2%29%5E2=24\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "There are 24 little cubies with only one side painted.\r<BR>\n" );
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document.write( "The number with two sides painted is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12%28n-2%29 ALIGN=MIDDLE  ALT=\"12%28n-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12%284-2%29=24 ALIGN=MIDDLE  ALT=\"12%284-2%29=24\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "The number with three sides painted is always 8. They are on the corners and that is true regardless of the cube size. \r<BR>\n" );
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document.write( "Those remaining are the ones in the center with no paint. That is\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28n-2%29%5E3 ALIGN=MIDDLE  ALT=\"%28n-2%29%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%284-2%29%5E3=8 ALIGN=MIDDLE  ALT=\"%284-2%29%5E3=8\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So, we have 24+24+8+8=64...as it should be.\r<BR>\n" );
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document.write( "Add up the formulas:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8%2B%28n-2%29%5E3%2B6%28n-2%29%5E2%2B12%28n-2%29 ALIGN=MIDDLE  ALT=\"8%2B%28n-2%29%5E3%2B6%28n-2%29%5E2%2B12%28n-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "A pattern. A binomial. Add these up and it reduces all the way down to\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n%5E3 ALIGN=MIDDLE  ALT=\"n%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Just as we expected. 4^3=64\r<BR>\n" );
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