document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=335127>Question 335127</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Alan, Ben and Cal are seated as shown with their eyes closed.  A  B  C ....Cal is sitting in the front, behind him, Cal, and behind him Alan (in train style).  Diane places a hat on each of their heads from a box they know contains 3 red and 2 blue hats.  They all open their eyes and look forward.\r<BR>\n" );
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document.write( "Alan is sitting behind Ben, who is sitting behind Cal.  Alan says; \"I cannot deduce what color hat I'm wearing\"  Hearing that, Ben says, \"I cannot deduce what color I'm wearing either.\"  Cal then says, \"I know what color I'm wearing!\"\r<BR>\n" );
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document.write( "How does Cal know the color of his hat? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #240196 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=240196\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> here's the deal:\r<BR>\n" );
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document.write( "There are 3 red hats and 2 blue hats.\r<BR>\n" );
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document.write( "A sits behind B sits behind C\r<BR>\n" );
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document.write( "All look forward.\r<BR>\n" );
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document.write( "A says he doesn't know what hat he is wearing.\r<BR>\n" );
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document.write( "B says he doesn't know what hat he is wearing.\r<BR>\n" );
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document.write( "C says he knows.\r<BR>\n" );
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document.write( "The color of the hat C is wearing has to be red.\r<BR>\n" );
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document.write( "Here's how:\r<BR>\n" );
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document.write( "Assume C has a red hat on.\r<BR>\n" );
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document.write( "This means that B could have a red or a blue hat on.\r<BR>\n" );
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document.write( "A looks and sees either 2 red hats or 1 blue and 1 red hat.\r<BR>\n" );
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document.write( "A can't determine what color hat he has on because he cannot know unless both B and C had a blue hat on, which they don't.\r<BR>\n" );
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document.write( "So A doesn't know which means that B and C either have 1 red and 1 blue or 2 red.\r<BR>\n" );
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document.write( "B looks at A and sees a red hat.\r<BR>\n" );
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document.write( "This means that B could have a red hat on, or a blue hat on, so he doesn't know either.\r<BR>\n" );
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document.write( "C knows that the only way A would know is if both B and C had blue hats.\r<BR>\n" );
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document.write( "C also knows that the only way B would know is if C had a blue hat on.\r<BR>\n" );
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document.write( "C concludes he has a red hat on.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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