document.write( "Question 1127420: Peter has many socks, all the same except that they are in five different colours. He is leaving to catch an early train to go on a business trip, and he does not want to wake his wife, so he packs in the dark. He needs eleven pairs of socks, each sock in each pair the same colour. How many socks must he take from his drawer to be sure of achieving this? \n" ); document.write( "
Algebra.Com's Answer #793002 by ikleyn(52782)\"\" \"About 
You can put this solution on YOUR website!
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\n" ); document.write( "Peter has many socks, all the same except that they are in five different colors.
\n" ); document.write( "He is leaving to catch an early train to go on a business trip, and he does not want to wake his wife, so he packs in the dark.
\n" ); document.write( "He needs eleven pairs of socks, each sock in each pair the same color.
\n" ); document.write( "How many socks must he take from his drawer to be sure of achieving this?
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\n" ); document.write( "\n" ); document.write( "It is easy for me to disprove the solution of the other person:\r
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\n" ); document.write( "\n" ); document.write( "         to have  11  socks matching,  the number of the taken socks must be at least  22.     (ha-ha-ha)\r
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\n" ); document.write( "\n" ); document.write( "         And  22  is the happiest case,  if you are lucky  11  times in a row\r
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\n" ); document.write( "\n" ); document.write( "So,  the correct solution  MUST  BE  different (!)\r
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\n" ); document.write( "\n" ); document.write( "                * * * THE  CORRECT  SOLUTION * * *\r
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document.write( "It is a nice entertainment problem, and if you solve it for the first time in your life,\r\n" );
document.write( "it is better do it step by step.\r\n" );
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document.write( "1) How many socks should he take to be sure that there is at least one good pair of the same color ?            \r\n" );
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document.write( "       In the worst  case, he will take 5 socks of different color,\r\n" );
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document.write( "       but any 6-th sock will match with one of 5, just taken.\r\n" );
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document.write( "       So, 6 socks is enough in this case.\r\n" );
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document.write( "2)   How many socks should he take to be sure that there are at least two good pairs of the same color ? \r\n" );
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document.write( "       In the previous case, worst case was 5 socks of different colors.\r\n" );
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document.write( "       After adding any 6-th sock, we have one good pair and match,\r\n" );
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document.write( "             but still may have 4 remaining socks of different colors.\r\n" );
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document.write( "       So, we should add the sock #7 to create possible worst case, and then add #8 to have a match guaranteed.\r\n" );
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document.write( "       So, the answer in this case is 8,  which is  \"add 2 to 6\".\r\n" );
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document.write( "3)   After that, the pattern is clear: to provide next match, we should add 2 socks from the drawer after every previous match.\r\n" );
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document.write( "4)  Following this pattern, I create the table below\r\n" );
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document.write( "        # of matching pairs    1    2     3    4     5     6     7     8     9     10     11\r\n" );
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document.write( "        # of socks to take     6    8    10   12    14    16    18    20    22     24     26\r\n" );
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document.write( "5)   ANSWER.  26 socks.\r\n" );
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\n" ); document.write( "\n" ); document.write( "The solutions and the answers of two other tutors, @math_helper and @additi123,
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