Any which way

one, a, an, or some; one or more without specification or identification:
if you have any witnesses, produce them. pick out any six you like.
whatever or whichever it may be:
cheap at any price.
in whatever quant-ty or number, great or small; some:
do you have any b-tter?
every; all:
any schoolboy would know that. read any books you find on the subject.
(following a negative) at all:
she can’t endure any criticism.
an unspecified person or persons; anybody; anyone:
he does better than any before him.
a single one or ones; an unspecified thing or things; a quant-ty or number:
we don’t have any left.
in whatever degree; to some extent; at all:
do you feel any better?
any which way, in any manner whatever; indifferently or carelessly:
doing your work any which way is just not good enough.
determiner

one, some, or several, as specified, no matter how much or many, what kind or quality, etc: any cheese in the cupboard is yours, you may take any clothes you like
(as pr-noun; functioning as sing or plural): take any you like

(usually used with a negative)

even the smallest amount or even one: i can’t stand any noise
(as pr-noun; functioning as sing or plural): don’t give her any

whatever or whichever; no matter what or which: any dictionary will do, any time of day
an indefinite or unlimited amount or number (esp in the phrases any amount or number): any number of friends
adverb
(usually used with a negative)

(foll by a comparative adjective) to even the smallest extent: it isn’t any worse now
(not standard) at all: he doesn’t care any

adj.

old english ænig “any, anyone,” literally “one-y,” from proto-germanic -ainagas (cf. old saxon enig, old norse einigr, old frisian enich, dutch enig, german einig), from pie -oi-no- “one, unique” (see one). the -y may have diminutive force here.

emphatic form any old ______ (british variant: any bl–dy ______) is recorded from 1896. at any rate is recorded from 1847. among the large family of compounds beginning with any-, anykyn “any kind” (c.1300) did not survive, and anywhen (1831) is rarely used, but oed calls it “common in southern [british] dialects.”

any day
any longer
any number of
any old
any port in a storm

also see:

at any rate
by any means
go to any length
in any case
under any (no) circ-mstances