Math Test

 So as you probably know, there's a college hockey tournament in Boston every year called The Beanpot.

The tournament, which has a men's side and a women's side, includes four schools: Harvard, Boston College, Boston University and Northeastern. The first-round pairings rotate each year, as opposed to having the same two teams meet year after year.

This year's men's winner was Northeastern, which defeated Harvard in a shootout earlier this week in the championship game. For official records, the game is considered a tie, but a winner had to be determined.

What's most amazing about that is that this was the 70th Beanpot and somehow, insanely, the first time that Harvard and Northeastern played in the final. How is that even remotely possible? 

What are the odds that four teams would be randomly split into two semifinals and that two of those four teams would never meet in the final until 70 years later? To find out the answer, TigerBlog reached out to Princeton resident math genius Thayer Patterson.

And while TB waits for Thayer to get back to him, here is some more stuff, including some numbers, for this Thursday:

* The Ivy League women's swimming and diving championships come to DeNunzio Pool this weekend. In fact, the event actually started last night with two Princeton relay wins, but it kicks into high gear this morning with preliminaries at 11 and finals at 6, a schedule that repeats itself tomorrow and Saturday.

This century, only Princeton, Harvard or Yale has won the title, and all-time only those three and Brown have ever won. The Tigers have won 23 times, with Harvard next at 15.

Perhaps more than any other year, though, this time around the field is pretty wide open, with a strong case to be made for any of four teams near the top, including Princeton. 

For more information, including schedule and video links, click HERE.

The men's championships are at Brown next weekend.

* This is the final week of the ECAC women's hockey regular season, and Princeton has locked up a spot in the eight-team playoffs, accomplished last weekend with a pair of overtime wins at Baker Rink. Princeton enters this weekend in sixth place, able to move up to fifth or down to seventh, depending on this weekend's results.

Princeton will definitely be on the road for the playoffs next weekend. Where? It's possible it could be Yale, Clarkson, Quinnipiac or Colgate. If it's Clarkson, it would be the second straight ride up there, as the Tigers are at Clarkson and St. Lawrence this weekend.

* Meanwhile, on the men's side, there are two weekends to go. 

Princeton enters its home weekend with Brown and Yale (7 tomorrow and Saturday) in seventh place, with home ice in the first round to go to teams five through eight, with the top four to earn a bye. The Tigers are at Union and RPI next weekend to wrap up the regular season.

Union is currently tied with Princeton at 23 points. RPI is in eighth, with 20. Check back next week to see where things stand, since too many teams are too closely bunched to make it make sense right now.

* In other hockey news, there is McKnight Pederson, a sophomore lacrosse defenseman. Due to injuries to the men's hockey team, McKnight will have a busy weekend, since he'll be practicing with the men's lacrosse team tomorrow afternoon, serving as the backup goalie for the hockey team tomorrow night, playing for the men's lacrosse team Saturday at 3 in the season opener against Monmouth and then rushing to Baker Rink for the Saturday night hockey game.

If you're wondering if Princeton has ever had someone play for two different teams in one day, TB knows of at least one — Jason Osier, who in 1997 played lacrosse in the afternoon and basketball and night.

As for the Pederson family, there will be three of them on Sherrerd Field Saturday, with McKnight and his older brother Beau (preseason first-team All-American) on the Princeton men's team and sister Lauren on the Virginia women's team. Virginia will be at Princeton on the women's side at noon.

* Finally, this is what Thayer had to say:

I think what you are asking is what would be the odds if each team were evenly matched every year so that each team has a 50% chance of winning any game they are in. There are 4 possible matchups of 4 teams. With equal probability, there would be a 25% chance of each matchup. So the probability that you would have 69 finals without that matchup would be like flipping a 75% Heads coin and getting 69 Heads in a row. So (0.75)^69. And then this year multiply that by 0.25 = 5.99 x 10^(-10), so 10 decimal places in front.