We've gotten through a moderate amount of competition. I'm not experienced enough to draw out the whole bracket on the computer, so I'll just list the results:

Round 1:
Prateek (1) beats Dmitriy (16)
Sarah (9) beats Robby (8)
Lily (4) beats Josh (13)
Pio (5) beats Samantha (12)
Kristen (3) beats Robert (14)
Matt (6) beats Kim (11)
Sam (2) beats Deep (15)
Lucas (7) beats Andrea (10)

Round 2:
Winners' bracket:
Prateek (1) beats Sarah (9) -> Sarah goes to Losers' bracket
Lily (4) beats Pio (5) -> Pio goes to Losers' bracket
Kristen (3) beats Matt (6) -> Matt goes to Losers' bracket
Sam (2) beats Lucas (7) -> Lucas goes to Losers' bracket

Losers' bracket:
Dmitriy (16) beats Robby (8) -> Robby is eliminated
Josh (13) beats Samantha (12) -> Samantha is eliminated
Kim (11) beats Robert (14) -> Robert is eliminated
Andrea (7) beats Deep (15) -> Deep is eliminated

Round 3:
Winners' bracket:
Prateek vs. Lily will take place first thing on Monday.
Sam (2) beats Kristen (3) -> Kristen goes to Losers' bracket, Sam goes to prefinal.
All four of these competitors get Round 4 off.

Losers' bracket:
Lucas (7) beats Dmitriy (16) -> Dmitriy is eliminated
Matt (6) beats Josh (12) -> Josh is eliminated
Pio (5) beats Kim (11) -> Kim is eliminated
Sarah (9) beats Andrea (10) -> Andrea is eliminated.

Rounds 4, 5, the 5th and 7th place matches, the semifinal and final will take place on Monday at lunch or after school.

Who is assured what: Kristen, Prateek and Lily all will get at least 6th place, but will get higher unless they lose out. Sam and the winner of Prateek/Lily are assured at least 3rd place. Everyone else is assured at least 8th place, and a spot on one of the teams.

Notes: Samantha, Robby and Robert forfeited both of their matches. Dmitriy and Sarah each offered to forfeit to Prateek to get those rounds over with (thanks to them). It is interesting that the remaining seeds are 1, 2, 3, 4, 5, 6, 7, and 9.

What will happen Monday:

Round 3 match: Prateek vs. Lily
Round 4 matches: Lucas vs. Matt, Pio vs. Sarah
Round 5 matches: Lucas/Matt winner vs. Prateek/Lily loser, Pio/Sarah winner vs. Kristen, Sam vs. Prateek/Lily winner (the prefinal)
7th/8th Place: Lucas/Matt loser vs. Pio/Sarah loser

Round 6 match: Lucas/Matt/Prateek/Lily winner vs. Kristen/Pio/Sarah winner
5th/6th Place: Lucas/Matt/Prateek Lily loser vs. Kristen/Pio/Sarah loser
Semifinal: Round 6 winner vs. Prefinal loser
Final: Semifinal winner vs. Prefinal winner
(Final 2): Final winner vs. Prefinal winner (The winner of the prefinal gets two chances in the final)

4th Place is the Round 6 loser, 3rd is the Semifinal loser, and 1st and 2nd are determined in the final(s).
1st and 2nd place join me on the first team. 3rd, 4th, and 5th make up the second team, and 6th, 7th and 8th make up the third team.

I plan on getting rounds 3, 4, and 5 and the 7th/8th place match done during lunch. The rest will be after school. We might hold a sort of "Fun Round" after the final between me and the rest of the first and second teams. It all depends on time.