Solution to Bracketology 2012
This puzzle is a straight up logic puzzle that revolves around the 2012 NCAA Men's Basketball tournament. We can use the clues along with the actual outcomes to fill out the bracket completely.
- I sent one first seed team to the final four, which would be my only glimmer of success → I sent 01 Kentucky to the Final Four
- I'd earn 192 in the finals + After the first round games, my championship winner had lost → 06 San Diego St. was my choice for champion
- I'd earn 192 in the semifinals → 06 Murray St. was the other team I sent to the finals
- I'd earn 144 in the regional finals → 05 Vanderbilt is the remaining team I sent to the Final Four
- All my 1/16 and 2/15 games were spot on → I chose 01 Syracuse, 01 North Carolina, 01 Michigan St., 15 Lehigh, 15 Norfolk St., 2 Kansas, 2 Ohio State all to win their first round games
- (A) If one of my chosen teams lost in the first round, I had them winning in the second round too. Therefore, all teams I had as losing in the second round must have actually won in the first round in real life → I chose 08 Iowa State, 04 Wisconsin, 03 Marquette, 03 Georgetown to win their first round games
- I'd earn 260 in the 3rd round, of which 72 comes from the Final Four teams, leaving four teams whose seeds sum to 47. But because after the results of the first round, I'd earn at most 128 in the 3rd round, two of my Elite 8 teams whose seeds sum to 27 must have lost in the first round. The only way to do this is with a 13 seed and a 14 seed ( my 15 and 16 seeds won in the first round ) → I sent 13 Davidson to the Elite 8
- The other two teams in my Elite 8 whose seeds sum to 20 must have actually won in the first round → I had 13 Ohio, 07 Gonzaga, and 14 South Dakota St. finishing my Elite 8
- Again, premise (A) above → I had 11 Colorado, 12 South Florida, and 05 New Mexico winning their first round games
- We have now identified 3 out of the 6 teams that I incorrectly chose to win in the first round. The seeds of the remaining 3 teams must sum to 32. Furthermore, since I chose upsets in 12 games, and only 10 upsets actually happened, these remaining 3 teams must be composed of 2 upsets (seed > 8) and 1 non-upset (seed ≤ 8). The only ways this can happen from the remaining unidentified games are 8+11+13 or 8+10+14 → I must have selected 08 Memphis, 12 VCU, 10 Xavier, 08 Kansas State, 08 Creighton, and 10 Purdue to win their first round games
- I have at most two incorrectly chosen first round teams per region → I selected 07 Florida, 11 Texas, 13 New Mexico St., and 03 Florida St. to win their first round games
- My teams that lost in the first round were also selected to win the second round → I selected 11 Texas, 08 Memphis, 13 New Mexico St. to win their second round games too
- I had the underdogs winning in the 2nd round games in the Midwest → I chose 08 Creighton and 10 Purdue to win their second round games
- My possible scores in the second round constrain the remainder of the bracket → I had 10 Xavier, 01 Syracuse, 07 Florida winning their second round games.
With the bracket filled out, we can then use the dollar amounts of each individual game wager to index into the name of the team I had winning that game. Working from top to bottom in each region in the order listed, we extract the letters:
ATENTHSEEDSOUTHREGIONATHLETEISA
The moniker for a member of Xavier's basketball team is a MUSKETEER.