Same as the cat thing, except that we now use the
universally
accepted phenomenon that if you put an even number of
socks in a washing machine, you get an odd number out.
Hence, any given sock can be considered to be entangled
during the spin cycle.

Baked by one of the greatest theoretical physicists of all time - John S. Bell - in a paper titled "BERTLMANN'S SOCKS AND THE NATURE OF REALITY," in Journal de Physique Colloques 42, C2 (1981). See link. Clicking on the pdf linked there is a must; then you can see Bell's drawing of professor Bertlmann wearing one pink sock and one not-pink sock. Bell posits that the socks' color are entangled. I suppose you are going to claim he got them out of Schrödinger’s Washing Machine.

Still [+]. There is no shame in being scooped by John Bell.

I infer from this socks then behave as a particle and a wave. This explains how when I was a kid my socks, like a wave, would flow to the toe of my gumboots

//my socks, like a wave, would flow to the toe of my gumboots//

[+], but if your socks are true quantum entities, they will be fermions or bosons. If bosons, then you will always find both socks together in the toe of one or the other gumboot. It is said that bosons undergo "bunching."

The state of one sock is easily determined by quantum
entanglement with the other. When one is dirty and lost,
the other is folded, clean, and in the drawer, and vice-
versa.