Math Diary Entry 1

This December I will be participating in the William Lowell Putnam Mathematical Competition. To put it shortly, the Putnam Competition. It's an extremely difficult competition. The average is 0/120. Yes, 0.

I have been working on a question from last year's competition, question B3. You can read it in the pdf. My professor and I sat in almost complete silence for about 30 minutes doing this question. All I have to say is that it's not as weird as you would think, mostly because you are thinking real hard. About every 5 minutes we would say something about the problem, then realize something else and sit again thinking.

Now in the competition, we have 6 hours, 2 3 hour sessions, to answer 12 questions. So you have about 30 minutes each problem, but in each round the questions get progressively harder.

So my goal is to answer at least one question.

Also, in contemplating this problem, I laid in bed this morning for about 40 minutes thinking about the question. I came up with something that I hope will help lead to a proof for question B3. If two teams won their only game on the same day, it would be impossible for both teams to only win one game, since they have to compete against each other, and thus someone ends up winning two games instead of just one. So I'm hoping when I tell my professor this it will help get to some answer.

I really want to solve this problem because it was like 1 of 2 problems that I fully understood on the 2012 Putnam competition.