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 #839944 by </B><A HREF=/tutors/aboutme.mpl?userid=ikleyn><B>ikleyn(52790)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ikleyn><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=ikleyn><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=839944\">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 a painting using two colors: it is the chessboard painting.\r<BR>\n" );
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document.write( "From the other side, one color does not produce any solution.\r<BR>\n" );
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document.write( "Hence, two colors is the least number of different colors that is needed.\r<BR>\n" );
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document.write( "It is a standard, traditional, complete and mathematically absolutely correct reasoning and a solution.\r<BR>\n" );
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document.write( "See similar solutions at this forum under these links\r<BR>\n" );
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document.write( "https://www.algebra.com/algebra/homework/word/evaluation/Evaluation_Word_Problems.faq.question.1096043.html\r<BR>\n" );
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document.write( "https://www.algebra.com/algebra/homework/Length-and-distance/Length-and-distance.faq.question.1095728.html\r<BR>\n" );
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document.write( "This problem is known for hundreds of years. With a similar solution, it is written and placed <BR>\n" );
document.write( "in hundreds of textbooks in Math in different languages, that are collections of entertainment problems. <BR>\n" );
document.write( "So far, I never heard  that somebody would be unsatisfied or expressed doubts in validity of this solution.<BR>\n" );
document.write( "In opposite, the normal human reaction is admiration that so simple and so elegant solution is possible.<BR>\n" );
document.write( "You are the first person who expresses your unsatisfaction &nbsp;(due to unknown reason). &nbsp;My congratulations &nbsp;(&nbsp;!&nbsp;)\r<BR>\n" );
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