Solution 1:

There's a lot of exciting possibilities listed on Wikipedia, but it sounds as if nobody knows for sure.

Solution 2:

Like Gaurav said, nobody knows for sure. Here is a well sourced and interesting article on the topic. Here the author writes about the impassioned responses that the article evoked from his readers.

Solution 3:

New research suggests the nine was just an arbitrary number.

A recent discovery of a whole six yards of this "Holy Grail among word sleuths" suggests the modern phrase is an example of "phrase inflation", similar to cloud nine's inflation from the earlier cloud seven and cloud eight.

Yale law librarian Fred R. Shapiro wrote in the Yale Alumni Magazine (Jan/Feb 2013):

[Bonnie] Taylor-Blake’s next discovery took the research in a completely unexpected direction. Searching Google News Archive, she found, in the sports section of the Spartanburg (South Carolina) Herald-Journal of May 7, 1921, an article about a baseball game between the Spartanburg Spartans and the Greenville Spinners. With it was a more detailed, at-bat-by-at-bat description of the same game. The headline of the detailed account? “The Whole Six Yards of It.”

That headline appears to use “the whole six yards” in exactly the same sense as we now use “the whole nine yards.” I found confirmation via the database Chronicling America. An article in the Mount Vernon (Kentucky) Signal of May 17, 1912, states: “But there is one thing sure, we dems would never have known that there was such crookedness in the Rebublican [sic] party if Ted and Taft had not got crossed at each other. Just wait boys until the fix gets to a fever heat and they will tell the whole six yards.” And again, in the June 28, 1912, issue: “As we have been gone for a few days and failed to get all the news for this issue we will give you the whole six yards in our next.”

Solution 4:

There is a high likelihood that it refers to nine yards of fabric. Nine yards of fabric was a common standard length for retail sale at least in the mid-to-late 1800s and into the early 1900s. http://esnpc.blogspot.com/2015/02/nine-yards-to-dollar-history-and.html