document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=793898>Question 793898</A>: <I><SPAN STYLE=\"word-break: break-all;\"> help ive got no idea where to start\r<BR>\n" );
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document.write( "There are 100 monsters. 38 of them are visible, the rest are invisible. Amongst the visible<BR>\n" );
document.write( "monsters, 16 glow red, 18 glow blue, 18 glow green, 7 glow red and blue, 5 glow blue and<BR>\n" );
document.write( "green and 6 glow red and green. (Note that \16 glow red\" should be interpreted as: 16<BR>\n" );
document.write( "monsters glow red, but each of those monsters is free to glow other colours too. The other<BR>\n" );
document.write( "numbers should also be interpreted in the same way).<BR>\n" );
document.write( "One day the monsters that simultaneously glow with all three colours, decide to join forces<BR>\n" );
document.write( "with the invisible monsters, to form a mighty army. How many monsters are in the army?<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #480591 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=480591\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The number of visible monster is said to be <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=38 ALIGN=MIDDLE  ALT=\"38\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "The rest of the 100 monsters is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=100-38=62 ALIGN=MIDDLE  ALT=\"100-38=62\"   DISABLED_style= \"max-width:90%; height:auto;\" >invisible monsters.<BR>\n" );
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document.write( "There are <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" > monsters that simultaneously glow with all three colors, and they are counted in all the other numbers given.<BR>\n" );
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document.write( "There are also <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=D ALIGN=MIDDLE  ALT=\"D\"   DISABLED_style= \"max-width:90%; height:auto;\" > monsters that glow with exactly 2 colors.<BR>\n" );
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document.write( "If you add<BR>\n" );
document.write( "the 16 monsters that glow red, plus<BR>\n" );
document.write( "the 18 monsters that glow blue, plus<BR>\n" );
document.write( "the 18 monsters that glow green<BR>\n" );
document.write( "you get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=16%2B18%2B18=52 ALIGN=MIDDLE  ALT=\"16%2B18%2B18=52\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "That count of 52 glowing monsters exceeds the number of visible monsters.<BR>\n" );
document.write( "If we were counting each visible monster just once we should add up to 38.<BR>\n" );
document.write( "That means that some monsters are being counted more than once in that total of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=52 ALIGN=MIDDLE  ALT=\"52\"   DISABLED_style= \"max-width:90%; height:auto;\" > because they glow with two or three colors at once.<BR>\n" );
document.write( "The difference, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=52-38=14 ALIGN=MIDDLE  ALT=\"52-38=14\"   DISABLED_style= \"max-width:90%; height:auto;\" > includes <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=D ALIGN=MIDDLE  ALT=\"D\"   DISABLED_style= \"max-width:90%; height:auto;\" > (each dual color monster counted once), plus <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x ALIGN=MIDDLE  ALT=\"2x\"   DISABLED_style= \"max-width:90%; height:auto;\" >  (2 extra counts for each triple color monster), so<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=14=D%2B2x ALIGN=MIDDLE  ALT=\"14=D%2B2x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Adding the numbers of monsters that glow with at least two colors at once we get<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7%2B5%2B16=18 ALIGN=MIDDLE  ALT=\"7%2B5%2B16=18\"   DISABLED_style= \"max-width:90%; height:auto;\" >. That includes <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=D ALIGN=MIDDLE  ALT=\"D\"   DISABLED_style= \"max-width:90%; height:auto;\" > (each dual color monster counted once), plus <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x ALIGN=MIDDLE  ALT=\"3x\"   DISABLED_style= \"max-width:90%; height:auto;\" > because each triple color monster is counted 3 times, once for each pair of colors.<BR>\n" );
document.write( "So <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=18=D%2B3x ALIGN=MIDDLE  ALT=\"18=D%2B3x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%2814=D%2B2x%2C18=D%2B3x%29 ALIGN=MIDDLE  ALT=\"system%2814=D%2B2x%2C18=D%2B3x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=18-14=4 ALIGN=MIDDLE  ALT=\"x=18-14=4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "That might army includes the 4 triple color monsters, plus the 62 invisible ones, for a total of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=62%2B4=highlight%2866%29 ALIGN=MIDDLE  ALT=\"62%2B4=highlight%2866%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28300%2C300%2C-15%2C15%2C-10%2C20%2C%0D%0Ared%28circle%28-5%2C0%2C8%29%29%2Cblue%28circle%285%2C0%2C8%29%29%2Cgreen%28circle%280%2C8.66%2C8%29%29%2C%0D%0Alocate%28-7%2C-1%2C7%29%2Clocate%286%2C-1%2C10%29%2Clocate%28-0.5%2C-1%2C3%29%2C%0D%0Alocate%28-0.8%2C3.5%2C4%29%2Clocate%28-0.3%2C11%2C11%29%2C%0D%0Alocate%28-5%2C6%2C2%29%2Clocate%284%2C6%2C1%29%2Clocate%28-11%2C16%2C62%29%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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