|MadSci Network: Engineering|
The basic problem is simple: there are two many 1 to 1 matchings, and so too many ways that at least one of a pair will be missing. One of the pair can be lost in one of several places: a) when you take them off and drop them on the floor b) when you move things around on the floor c) when you scoop them up and drop them in the laundry enclosuer d) in the laundry room e) in the washer f) in the dryer Naturally, messier places make it easier for a lost sock to find a hiding place. So, if the floor of your room is messy -- well, it can be the safe haven for lots of errant socks. Anyway, let's go through the probabilistic math: If you only had one pair of socks, and the chance of losing one of the pair was, say, 5%...then there are two ways you could have a missing sock: you could be missing the first or the second sock. The probability of not missing a sock is .95 x .95 = 90.25%, so there is a 9.75% chance of missing a sock. Now let's imagine you have two pairs of socks, each matched. Because each pairs of socks are matched, losing any one of the four socks causes a problem. So, the chance of not missing a sock is .95^4 = .8145, giving a19.55% chance of missing at least one sock and therefore having the problem. With 4 pairs of socks, the probability of having this problem goes to 34%, and with 8 pairs of socks, the probability goes to 56%. So, with 8 different pairs of matched socks, you are more likely than not to have the problem of thinking "the dryer ate my sock". Now -- what happens if you don't buy MATCHED socks? What happens if you buy 8 pairs of socks, all of the same style and color? Then, you no longer have to spend time finding the matched colored/style socks...and you no longer get frustrated when you can't find the other blue pair of socks among all the greys and blacks and such. Anyway -- here are two sites on this problem...one intended to explore the humor involved in this problem, the other elaborating on the efficiency involved in the solution proposed above: The Bureau of Missing Socks Buying a pair of socks is foolish
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