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If you are making an RPG or RTS game, chances are that you will need to use some kind of pathfinding and/or local avoidance solution for the behaviour of the mobs. They will need to get around obstacles, avoid each other, find the shortest path to their target and properly surround it.
I hope I can contribute something new to this problem. I noticed that all of the answers neglect the fact that there are two points where you can perform preprocessing, without slowing down your overall laundry performance. Also, we don't need to assume a large number of socks, even for large families. Socks are taken out of the drawer and are worn, and then are tossed in a place (maybe a bin) where they stay before being laundered.
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