That's not how hats work.

I investigated an idiom the other day, prompted by an idle musing on Unfogged.  Instead of a short, comprehensible story, I got an incestuous slurry of modification and repurposing.  Here goes.

The phrase as cited was "take X apart six ways from Sunday."  My memory and a couple of quick searches confirmed this was just one of many variations including changing up the number of ways, the preposition before "Sunday," and the verb used.  The verb is normally on the violent side - "beat," "screw," "knock," etc.; and often still combative even when used cerebrally - "analyze," "vet," "take apart."  (It can also just mean "all over," as with "leaves lying..." or "his hair went...".)   The preposition can be "from," "to," or "till."  The number used varied all over.  Quickly falling into the research trance, and failing to find a satisfactory explanation (though there were some pretty outlandish ones), I drew up a spreadsheet based on Google Books search results, to try to figure out which came first.

Number	"From"	"To"	"Til" / "Till"
two	6	7	0
both	3	4	1
three	112	84	0
four	87	76	5
five	60	56	0
six	1260	1430	37
seven	314	218	8
eight	116	113	5
nine	178	160	15
ten	66	80	2
eleven	1	0	0
twelve	22	16	1
thirteen	1	4	4
fourteen	17	8	0
fifteen	4	6	0
sixteen	19	21	0
seventeen	24	2	2
eighteen	5	4	2
nineteen	0	0	0
twenty	8	15	17

My preliminary conclusions from this table were:

• There's a lot of diversity; no one phrasing is dominant.
• Neither is one phrasing chronologically dominant. Most of Google Books's earliest citations were no earlier than the early 20th century; the exceptions were "nine ways from Sunday" (1828), "seven ways to Sunday" (1893), and "fourteen ways from Sunday" (also 1893).
• Alliteration seems to inform the popular choice - the predominance of "six" is inconclusive as that could be the original term, but the spikes at "sixteen" and "seventeen" (and possibly "twelve" and "twenty") probably admit of no other explanation.
• Playfulness also seems to inform choices, leading to the wide variety of numbers used, probably for the novelty value. (Higher round numbers like "forty," "fifty," "hundred," and "thousand" are also used, but I left them out for a shorter table.)
• "Til" is definitely the most modern; it wasn't cited before 1941.

But the early citations gave me no clue as to the actual origin of the phrase.  Even in the late 19th century, people seemed to be using it much as they do now, without having to explain it.

At this point, some other resource than Google Books had to take over.  I went to the university library's slang and idiom section, and after going through several dictionaries with no luck, I finally found a vital clue:

Look nine ways for Sunday[s].  To squint : nautical : from ca. 1850; ob.  Ex the C. 16-18 coll. look nine ways confused with the dial. look both (later all) ways for Sunday. 

-- A Dictionary of Slang and Unconventional English, Eric Partridge.  New York: MacMillan Publishing Co., Inc., 1970, p. 494.)

This used for, which I hadn't thought to look up!  I appended to the table:

Number	"From"	"To"	"Til" / "Till"	"For"
two	6	7	0	261
both	3	4	1	242
three	112	84	0	66
four	87	76	5	35
five	60	56	0	18
six	1260	1430	37	198
seven	314	218	8	284
eight	116	113	5	1
nine	178	160	15	210
ten	66	80	2	1
eleven	1	0	0	2
twelve	22	16	1	1
thirteen	1	4	4	0
fourteen	17	8	0	0
fifteen	4	6	0	0
sixteen	19	21	0	5
seventeen	24	2	2	2
eighteen	5	4	2	0
nineteen	0	0	0	0
twenty	8	15	17	7

Now, I thought, we're getting somewhere.  "For"'s citations are leaps and bounds earlier in time - 1770, 1858, 1824.  And "both" and "two" are not only much higher relative frequency than with the other prepositions, but are the only ones with 18th century citations, making me think they're the original.

Further explanations of that phrase "look both ways" made me think that either that or "look nine ways" was the original phrase.  A number of late 19th-century works cite a free translation of Erasmus's Apophthegms by Nicholas Udall  from 1564, which, quoting the Iliad, book 2, lines 212-219, said "Squyntyied he was, and looked nyne waies," where the corresponding original Greek was just a single word meaning "squinting."  Obviously people weren't quoting that translation, but it does point to the antiquity of the phrase.  I suspect "for Sunday" was added either for the rhyme ("for Sundays" was also common), or to incorporate a popular superstition that "a child born on that day is sure to squint, because it must look both ways for Sunday."  It's a weird enough idea that I could well imagine people making it up facetiously based on the phrase. (Incidentally, the verb "squint" to me just means to scrunch one's eyes up, but in the past it referred to strabismus, or being wall-eyed or lazy-eyed.)

How, then, did it lose the "look," and come into its modern usage as an emphatic phrase?  The following quote seems to be the missing link:

There is nothing more wicked than trifling with the national currency, and we shall look into the Parlour ourselves, and Parlay, as Inspector Bucket says, in a way that will make the Directors look nine ways for Sunday.

--“A Rating for the Bank Raters,” in Punch, or the London Charivari, January 30, 1864, p. 43

Here's another, more analytical but looking back to the same era:

…Our English slang equivalent [of the contemporary American “to give any one fits”] would be ‘I’ll make him look nine ways for Sunday”—that is, I presume, for Sabbath rest.  The literary reader will immediately recall here the introduction of this expression into a description (in the classical page of Punch nearly thirty years ago) of a fight between Tom Sayers and Bob Travers, where we were told how Tom gave Bob a straight one which

            Made him look nine ways for Sunday and finally fail to perceive it.

--“Americanisms,” Richard Proctor, in Knowledge, March 1, 1887 (vol. 10, p. 114).

 And one last in exactly the same sense, interestingly compiled by Yeats:

Big Frank Farrell, the miler of Ballyboulteen, got a prod backwards that brought a hullabaloo out of him you might hear at the other end of the parish.  One got a slice of a scythe, another a whack of a flail, a third a rap of a spade that made him look nine ways at wanst.

--Fairy and Folk Tales of the Irish Peasantry, William Butler Yeats, 1888.

Looking holistically at all my evidence, I propose the following evolution:

1. The saying "look both ways" at first described strabismus very matter-of-factly.  It was elaborated on with "for Sunday," possibly because of the superstition (or who knows, the superstition could have been made in response to the phrase.)
2. For purposes of color, the number was varied - six, seven, and nine being the most common at first.  This didn't keep people from having the original meaning in mind.
3. In the mid-19th century, people started nesting the phrase into "to make someone look nine ways for Sunday" meaning to knock someone silly.
4. The nested use took over as the original one dwindled.
5. It became unnecessary to say "look," because "[number] ways for Sunday" was enough colorful verbiage to communicate the concept efficiently.
6. Over the 20th century, people completely forgot the original meaning, so it was just an emphatic, standalone adverbial phrase.  With the preposition no longer conveying anything in particular, it became more and more freely swapped out with others (from, to, till).  A broader range of numbers also came to be used.

Innovation piling on innovation, to the point of unintelligibility.  What a language we speak.

As a supplementary note, people seemed to start to say "squint (number) ways" for a time in the 19th century.  Possibly that was a transitional measure as "squint" acquired its modern meaning.  Some books of rhetoric then used this phrase to name a clause that could be attached equally well to the preceding or following clause, therefore "looking both ways," and creating ambiguity.  An example was "Though some of the European rulers may be females, when spoken of altogether, they may be correctly classified under the denomination 'kings.'"  The term "squinting modifier," has survived all the way to modern SAT prep books, which even retain the explanation "because they look both ways at once," though clarifying the meaning with "wall-eyed."