document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1203231>Question 1203231</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Each edge and diagonal of a regular hexagon (15 in total) is colored red or black such that the hexagon appears unchanged when rotated by 60 degrees clockwise about its center. How many such colorings are possible? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #838620 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=838620\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "There are 15 line segments to be colored:<BR>\n" );
document.write( "(1) 6 edges<BR>\n" );
document.write( "(2) 3 diagonals that connect opposite vertices<BR>\n" );
document.write( "(3) 6 other diagonals<br><BR>\n" );
document.write( "For the appearance of the figure to be unchanaged when it is rotated by 60 degrees, all segments of the same type must be the same one of the two colors.<br><BR>\n" );
document.write( "So the number of different colorings is 2*2*2 = 8.<br><BR>\n" );
document.write( "ANSWER: 8<br><BR>\n" );
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