According to Mathematicians, There Are 177,147 Ways to Tie a Tie

If you are so unfortunate as to have a job that requires you to wear the cursed things, then maybe you should try a different knot in your tie. You can try these fancy ones, like the hoity-toity Eldredge Knot. But your possibilities don’t end with just a few that you’ve encountered online.
According to researchers led by Mikael Vejdemo-Johansson of the of the KTH Royal Institute of Technology in Sweden, there are 177,147 potential variations of the knotted tie. They built on the work of previous mathematicians who concluded that there were only 85 possibilities. To Vejdemo-Johansson and his colleagues, this seemed to be too small a number:

Vejdemo-Johansson apparently came to believe that the number produced by Mao and Fink was too small after noting the unique tie knot in the movie "The Matrix Reloaded"—a knot that didn't appear in the researchers list, which meant something wasn't quite right. In reexamining the criteria that Mao and Fink used for inclusion, they noted the pair restricted the number of tucks that would occur at the end of the tie tying, to just one. The pair, it was noted, also assumed that any knot created would naturally be covered in part by a flat section of fabric. Also, they restricted the number of windings that could be made to just eight, believing any more than that would cause the tie to become too short.

After devising new ways of expressing tie-tying mathematically, they crunched their numbers and came up with a result of 177,147.