document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1201527>Question 1201527</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Below is 4*4*4 cube. Matuk painted all six faces purple. when it dried he separated the small cubes and then glued the small cubes together with yellow glue to make a solid block. Before the glue dried he pushed out all the blocks which had purple paint on only one face. He pushed out from the front first. Then he pushed out the blocks from the side then the blocks form the top. How many cubes did he push out?\r<BR>\n" );
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document.write( "a)32   b) 24    c)64     d)48 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #835932 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=835932\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "OMG!!!<br><BR>\n" );
document.write( "I am constantly astonished at how poorly written some of the math problems are that I see posted to this forum....<br><BR>\n" );
document.write( "In this problem, when he separated the small cubes and then glued them together to form \"a block\", it does not say that that \"block\" was again a cube.  And if it was a cube, it doesn't say that the small cubes were back in their original places, so we have no idea where the purple faces of the cubes are.  And that of course makes it impossible to solve the problem, because we don't know which cubes to push.<br><BR>\n" );
document.write( "So we have to ignore the significant shortcomings in the statement of the problem and assume that the reconstructed \"block\" was again a cube, with all the small cubes in their original places.<br><BR>\n" );
document.write( "Given that, I interpret the problem differently than the other tutor.<br><BR>\n" );
document.write( "When we push all the small cubes that show a purple face from the front, then from the side, and then from the top, we push out not only the 4 cubes in the center of each of the 6 faces; we also push out the 2x2x2 block of cubes that is the \"center\" of the 4x4x4 cube.<br><BR>\n" );
document.write( "So the number of small cubes he pushed out is<br><BR>\n" );
document.write( "6(4) + 2*2*2 = 24+8 = 32<br><BR>\n" );
document.write( "ANSWER: a) 32<br><BR>\n" );
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