I cannot tell you how many times I've had to deal with this in my lifetime and how most people cannot grasp the beauty of the mathematics behind "the bracket." If you know how a "bracket" is supposed to "work" you can draw up a 16, 32, 64, hell, a 128 person bracket on any piece of paper, whiteboard, chalkboard, etc. And the problems usually occur when you get 1 or 2 more people than the normal bracket is built for. 5 people or 9 or 10 people or 17 people. I've dealt with this in dart tournament, pool tournament, BJJ tournament, etc. I've actually been a COMPETITOR at a BJJ tournament when I tried to explain to them that they had to re-do the brackets because there was a late entry and we now how 9 competitors. "No we don't? Well just put him here at the bottom."
"No...that won't work."
"Sure it will. Look, we'll just draw a line and he'll fight the winner of this fight."
"No...that won't work. The winner is supposed to fight the winner of THAT fight."
"Oh...well what do we do?"
"You go to a 16 person bracket."
"But we've only got 9?"
"Yes...which is exactly why you now have to go to 16." (I draw a 16 person bracket and he starts numbering them down the page 1 fighting 2, 3 fighting 4...)
"No, no, no. 1v16, 2v15 at the bottom of the page, 3v14 just below the middle, 4v13 just above." (Then he starts filling in the names down the page 1 and 16 and 8 and 9.)
"No, no, no. You don't have a 16, you've only got 9. Just fill in names next to the numbers 1 through 9."
"But look at all those byes?"
"Yeah, so? They will all be gone after ONE round. Then you will have a nice full bracket of 8. You basically have one play in match here at 8v9."
"Hmm, that looks like it will work?"
"Trust me, it'll work."
It got to the point that I will actually bring blank brackets of various sizes to tournaments that I'll go to...but it's funny to watch some Brazillian guy say I'm full of shit when I try to help him. So I sit back and watch his bracket blow up and listen to everyone yell at him and how come he didn't listen to old guy who seemed like he knew what he was talking about.
There are so many fun little facts about bracket making I wish I knew how to write proper mathematical notation on Sherdog. But trust me, once you see the math behind it, you can make a bracket of almost any size right on the spot. Even double elimination.