11 individual shoes, for if you picked up only 10, you could possibly pick 10
left shoes and no right shoes, or vice-versa.  But if so, the 11th one has to
match one of the other 10.

For your information:

 If you pick          then the probability of
this many shoes,     getting one matched pair is

       1                        0
       2                     1/19 = .053
       3                     3/19 = .158 
       4                   99/323 = .307
       5                  155/323 = .480
       6                  211/323 = .653
       7                  259/323 = .802
       8                3815/4199 = .909  
       9                4071/4199 = .970 
      10              45933/46189 = .994 
      11                        1 

If you pick 6 shoes out of the 20 you are more likely than 
not to have picked a matching part.



Edwin