document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1210234>Question 1210234</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Vera has 20 white socks, 21 black socks, 22 brown socks, 23 blue socks, 24 red socks, and 25 green socks. How many socks (at a minimum) must she pull out of her sock drawer to ensure at least six matching pairs of different colors?<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #851711 by </B><A HREF=/tutors/aboutme.mpl?userid=ikleyn><B>ikleyn(52781)</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=851711\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> .<BR>\n" );
document.write( "Vera has 20 white socks, 21 black socks, 22 brown socks, 23 blue socks, 24 red socks, and 25 green socks. <BR>\n" );
document.write( "How many socks (at a minimum) must she pull out of her sock drawer to ensure at least six matching pairs <BR>\n" );
document.write( "of different colors?<BR>\n" );
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document.write( "In the worst case, Vera will take 25 green socks, 24 red socks, 23 blue socks,<BR>\n" );
document.write( "22 brown socks and 21 black socks - in all, 25 + 24 + 23 + 22 + 21 = 115 socks.\r<BR>\n" );
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document.write( "   &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Notice that here I list the socks in the reverse order - <BR>\n" );
document.write( "   &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;according to their numbers of each color in the DESCENDING order.\r<BR>\n" );
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document.write( "Then she will have a lot of matching pairs of 5 colors (green, red, blue, brown and black), <BR>\n" );
document.write( "but still will NOT have 6 matching pairs of different color.\r<BR>\n" );
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document.write( "But after that, any two next socks will create the required 6-th pair of the white color.\r<BR>\n" );
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document.write( "So, the minimum number of socks Vera should draw from the drawer is 115 + 2 = 117,<BR>\n" );
document.write( "to have 6 guaranteed matching pairs of 6 different colors.\r<BR>\n" );
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document.write( "My answer coincides with the answer by @CPhill, but explanation/reasoning/logic<BR>\n" );
document.write( "is slightly different (more straightforward, in order for do not confuse a reader).\r<BR>\n" );
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document.write( "Solved.\r<BR>\n" );
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