Question 1054507
(1)
You want either 2 black socks or 2 blue socks
The WORST case for 2 picks is:
[ blk ] & [ blu ]
The 3rd pick guarantees you will have 1 pair
( either [ pair of blk ] or [ pair of blu ] )
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(2)
You want either [ 2 pairs of blk ] or [ 2 pairs of blu ]
The WORST case for picks is:
[ blk ], [ blu ], [ blu ], [ blk ], [ blu ], [ blk ]
in any order, so
[ blk ], [ blk ], [ blk ], [ blu ], [ blu ], [ blu ]
So, you have made 6 picks and you still don't
have 2 pairs of the same color.
The 7th pick guarantees in this worst case
you will have 2 pairs of the same color
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(3)
You want 1 pair of black socks
The worst case is:
[ 5 blu ] 
The 6th pick guarantees you will have 1 pair
of black socks
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Note that any other combination for the 1st 5 picks
except [ 5 blu ] will give you at least [ 2 blk  ] socks