document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=982390>Question 982390</A>: <I><SPAN STYLE=\"word-break: break-all;\"> An eyebrow number is an arrangement of the numbers 1, 2, 3, 4 and 5 such that the second and fourth numbers are each bigger than both their immediate neighbours. For example, (1, 3, 2, 5, 4) is an eyebrow and (1, 3, 4, 5, 2) is not. The number of eyebrow is<BR>\n" );
document.write( "A. 16<BR>\n" );
document.write( "B. 12<BR>\n" );
document.write( "C. 15<BR>\n" );
document.write( "D. 24<BR>\n" );
document.write( "E. 18 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #603226 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=603226\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> I would say there are <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%2816%29 ALIGN=MIDDLE  ALT=\"highlight%2816%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > eyebrow numbers.<BR>\n" );
document.write( "Here is why:<BR>\n" );
document.write( "The lesser of the second and fourth numbers must be 3 or greater,<BR>\n" );
document.write( "because it must be greater than two immediate neighbors,<BR>\n" );
document.write( "and those immediate neighbors could not be smaller than 1 and 2.<BR>\n" );
document.write( "If 3 is in one of those two special places (the second or the fourth place),<BR>\n" );
document.write( "numbers 1 and 2 must be flanking it,<BR>\n" );
document.write( "leaving numbers 4 and 5 to fill the other two places,<BR>\n" );
document.write( "and number 4 must be at one end, next to number 5,<BR>\n" );
document.write( "which would be in the other of those two special places (the second or the fourth place).<BR>\n" );
document.write( "So the eyebrow arrangement would look like one of these <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2 ALIGN=MIDDLE  ALT=\"2\"   DISABLED_style= \"max-width:90%; height:auto;\" > patterns:<BR>\n" );
document.write( "_ 3 _ 5 4 or 4 5 _ 3 _ .<BR>\n" );
document.write( "The numbers 1 and 2 go in the blank places, in that order, or in the reverse order.<BR>\n" );
document.write( "With <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2 ALIGN=MIDDLE  ALT=\"2\"   DISABLED_style= \"max-width:90%; height:auto;\" > choices for the order of 1 and 2,<BR>\n" );
document.write( "and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2 ALIGN=MIDDLE  ALT=\"2\"   DISABLED_style= \"max-width:90%; height:auto;\" > patterns to fill,<BR>\n" );
document.write( "we get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2A2=red%284%29 ALIGN=MIDDLE  ALT=\"2%2A2=red%284%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > such arrangements.<BR>\n" );
document.write( "If the lesser of the second and fourth numbers is not 3, it must be 4.<BR>\n" );
document.write( "In that case the possible patterns are<BR>\n" );
document.write( "_ 4 _ 5 _ or _ 5 _ 4 _ ,<BR>\n" );
document.write( "each with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3 ALIGN=MIDDLE  ALT=\"3\"   DISABLED_style= \"max-width:90%; height:auto;\" > blank spaces to be filled by the numbers 1, 2, and 3 in any order.<BR>\n" );
document.write( "There are <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2A2=6 ALIGN=MIDDLE  ALT=\"3%2A2=6\"   DISABLED_style= \"max-width:90%; height:auto;\" > possible orders for the numbers 1, 2, and 3,<BR>\n" );
document.write( "which applied to each of those <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2 ALIGN=MIDDLE  ALT=\"2\"   DISABLED_style= \"max-width:90%; height:auto;\" > patterns,<BR>\n" );
document.write( "gives us <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2A6=green%2812%29 ALIGN=MIDDLE  ALT=\"2%2A6=green%2812%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > eyebrow arrangements.<BR>\n" );
document.write( "The total number of eyebrow arrangements is then<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=red%284%29%2Bgreen%2812%29=highlight%2816%29 ALIGN=MIDDLE  ALT=\"red%284%29%2Bgreen%2812%29=highlight%2816%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );