<PRE><B>Question 1204579</B>
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The statement of the problem makes it impossible to answer the question.&lt;br&gt;
If in fact there are exactly nine pairs of socks of different colors, then the worst case is that he first picks one sock of each of the nine colors; then each of the next six socks he picks will make a matching pair.  That makes 9+6 = 15 socks to guarantee that he will have six pairs.&lt;br&gt;
(one possible) ANSWER: 15&lt;br&gt;
But the problem only says that there are &quot;many&quot; socks.&lt;br&gt;
Consider the absurd case in which there are 8 pairs of socks of different colors and 100 socks of a ninth color.  Then the worst case would be that he again first picks one sock of each of the nine colors.  Then the tenth sock he picks will make the first matching pair.  But after that the worst case would be that he then picks only socks of the last color.  He needs five more matching pairs, which means he would have to pick ten more socks of that color.  In that case, the number of socks he would have to pick to guarantee having six matching pairs is 9+1+10 = 20.&lt;br&gt;
Upon first reading the problem, I was immediately suspicious of the &quot;many&quot; socks, suspecting that that wording would make it impossible to answer the question -- and indeed that was true.&lt;br&gt;
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Tutor @ikleyn jumps at every chance she can find to disparage responses from other tutors.  But often her remarks indicate she is not reading those responses.&lt;br&gt;
As my response states, 15 socks are enough to guarantee 6 matching pairs IF THERE ARE EXACTLY 9 MATCHING PAIRS TO CHOOSE FROM.&lt;br&gt;
And, as she states in her &quot;corrected&quot; response, 20 socks must be chosen if there are more socks than just 9 matching pairs -- which is exactly what my response says.&lt;br&gt;
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To tutor @ikleyn....&lt;br&gt;
What a lame response to my post about your comment regarding my post.  You say you have an absolute ear for math; too bad your English is not very good, and/or that you can&#39;t read.&lt;br&gt;
My response clearly stated that the answer was 20 if we don&#39;t know how many total socks are in the drawer, and that the answer was 15 if there were exactly 9 pairs of matching socks.&lt;br&gt;
Your suggestion that there was anything wrong with my response is absolutely unfounded.&lt;br&gt;
Grow up and stop feeling like you need to show you are better than everyone else.&lt;br&gt;
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