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s is exactly what I do I make piles dependent on the style of the opening of the sock
 (I only have white), that hether sorting is beneficial or not is dependent on the problem 
domain, specifically on the topography of the phase space of the primary grouping 
criterion. As a counterexample to your statement, almost all my socks are in some 
variation of black, so the primary grouping criterion is shape instead - and a quick
 way to determine a on length". One could form piles for each millimeter of length, 
though. Each pile is addressable in O(1) so our distribution scheme still works and 
should be faster than sorting (actually, we are almost sorting but only by  well, I 
would say it's because a) humans put a lot of emphasis on ordering (as e.g. the Ultimatum
 Game experiments show), b) humans have very powerful, parallelized optical 
recognition abilities - seeing a row of socks pulled out of a pile, sorted by length,
 you probably would be immediately able to place the next sock out of the pile
 in the "right" spot. The problem is, the question as currently posted lacks clarity 
in one regard: do we treat humans as actual biological entities (with all the possible
 optimizations), or as bio-robots without How many times will you have to 
"Recursively apply this scheme" "until you have distributed all socks onto very 
small piles that you can visually process immediately"? I would calculate that as 
O(n log n). If my calculation iwell need only one step of distribution.; Asymptotic c
omplexity aside, I'd argue that distribution onto piles is I've tried this with my socks 
(I've got easily 30+ pairs) and man it is FAST. One problem I've found is when I can't 
have a good enough hash algorithm (I've got lots of white socks without any pattern) 
so it becomes hard. distinguishable by some attribute? There must be something you
 can distribute them on. Otherwise, you could just form pairs arbitrarily.are 
distinguishable but not on a fast glance. Comparing with file hashing, it is like th
e colored socks are a 100KB file and the white ones are 1GB files, it takes much longer
 to analyze. What I do on practice is to use different socks anyway,this satisfies the 
logarithmic space limit depends on the quality of the hash function. Let's say there is
 a perfect hash...it would take O(n) memory to remember which trait is associated with 
which bucket. This isn't an issue with an integer hash as you don't need to keep a table 
of values to buckets (you just apply some arithmetic) but it's an issue here. If you don't 
keep a lookup table in memory you need to do a scan of all the buckets, which (again, 
depending on the quality if the hash) could be no better than just scanning the pile