document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1203985>Question 1203985</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The interiors of all unit squares of a 10 by 10 board are to be painted. Any two squares that have a side in common will be painted with a different colour of paint. What is the least number of colours that will be needed?\r<BR>\n" );
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document.write( "I am not satisfied with the existing solution on the Algebra.com website. It is far too simple and is not \"mathematically\" conveyed in any manner. Of course, this is a marvelous free service, so my feedback might be taken with distaste, and I apologise for that, but if someone can give a more mathematical solution, I would really appreciate it.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #839945 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20850)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathLover1><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=MathLover1><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=839945\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> \r<BR>\n" );
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document.write( "There is only one rule\r<BR>\n" );
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document.write( "Two sections that share a common edge cannot be colored the same!\r<BR>\n" );
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document.write( "Having a common corner is OK, just not an edge.\r<BR>\n" );
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document.write( "Let's start with a simple pattern like a group of nine unit squares:\r<BR>\n" );
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document.write( "<a  rel=nofollow HREF=\"https://ibb.co/LCpRTCK\"><IMG STYLE=\"max-width:80%;\" src=\"https://i.ibb.co/LCpRTCK/coloring-1.gif\" alt=\"coloring-1\" border=\"0\"></a>\r<BR>\n" );
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document.write( "How many colors do you need to color the pattern of nine squares?\r<BR>\n" );
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document.write( "You could use nine different colors, but could make do with as few as two:\r<BR>\n" );
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document.write( "<a  rel=nofollow HREF=\"https://ibb.co/ChPmdsP\"><IMG STYLE=\"max-width:80%;\" src=\"https://i.ibb.co/ChPmdsP/coloring-2.gif\" alt=\"coloring-2\" border=\"0\"></a>\r<BR>\n" );
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document.write( "it will be same for 10 by 10 board, so you will need <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=two ALIGN=MIDDLE  ALT=\"two\"   DISABLED_style= \"max-width:90%; height:auto;\" > colors\r<BR>\n" );
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