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Household mathematics

I have figured out why I hate folding socks---it's a simple problem of mathematics.

7 days x 2 feet x 5 people = 70 socks---not counting all the times that Amanda loses her socks between outings and needs a new pair.

The total number of possible pairs of socks is 70x69/2=2415. Given a random sock pick, the chance that you pick out the pair for that sock is 1 in 69. Once you've got that pair, the chance you pick out a pair on the next two grabs is 1/67... Assignment: what is the chance that, reaching randomly into the bin each time, you come up with exactly the right pairing of socks?

If I had the time and no toddler, I could figure out the average time it would take you to pair up all the socks (someone has surely already done this). This doesn't even take into account all the lone socks that simply have no mate, no matter how many times you reach into the bin.

I realize that in real life the grabs are not random (you won't accidentally grab Eleanor's purple sock when you are looking for Mama's black sock). I have also made the problem easier by not sorting any of Michael's socks: I put them all in a drawer and he sorts them as he puts them on. I realize that I could also make this easier by buying all one kind of sock for each person: all purple for Eleanor, all pink for Amanda, etc. I'm not ready to do that yet (socks have been the one place I have felt free to express myself in clothing), but after thinking about the mathematics, I'm taking it under advisement.
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Anonymous said…
Well, perhaps when Luke is 5 he will opt to wear the same socks for days in a row like my kid does. Gross, but it does cut down on laundry...

FNDP
January 29, 2009 at 6:30 AM
mathmom said…
FNDP: One can only hope =)
January 29, 2009 at 8:31 AM
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