Posts Tagged ‘Putnam’

2008 Putnam

December 7, 2008

Godzilla using a calculatorThe 2008 William Lowell Putnam Mathematical Competition officially took place this weekend! Yup, six hours of grueling math problems. We had a record number of students take it this year: 21! [That’s just 21, not 21 factorial. That would be an impressive number.]

Here’s one of the videos that our students watched while they were gathered around my dining room table Friday night eating dinner (because we totally bribe our students with food: dinner the night before at my house, bagels for breakfast, and lunch at the local pub in between the two three-hour sessions). It’s “I Will Derive” and I know it’s made its way around the internet, but I still think it’s fabulous:

And here’s the problem (A2) that caused the most discussion over lunch:

Alan and Barbara play a game in which they take turns filling entries of an initially empty 2008×2008 array. Alan plays first. At each turn, a player chooses a real number and places it in a vacant entry. The game ends when all the entries are filled. Alan wins if the determinant of the resulting matrix is nonzero; Barbara wins if it is zero. Which player has a winning strategy?

Here’s my favorite problem (A1) because I was able to solve it right away and do you know how often that happens? Not very.

Let f : R2 -> R be a function such that f(x,y)+f(y,z)+f(z,x)=0 for all real numbers x,y, and z. Prove that there exists a function g : R->R such that f(x,y) = g(x)-g(y) for all real numbers x and y.

You can see the rest of the problems here, and pretty soon you should be able to find the answers hereEdited Monday 12/8 to add: yes, the answers are posted!

No, of course Godzilla didn’t really use a calculator on an exam. He’s a stickler for following the rules.

It’s Putnam Saturday!

December 1, 2007

Today is the day of the 67th Annual William Lowell Putnam Mathematical Competition, offered all over the United States and Canada. According to the official website, Mr. Putnam was a strong believer in the value of team competition and so after his death his widow (Elizabeth Lowell Putnam) developed a trust fund which supported some intercollegial competitions. The first one was not in mathematics at all, but in English! The MAA took responsibility for the Putnam Competition after Mrs. Putam’s death in 1935.

Everyone who takes the Putnam these days takes it in two 3-hour blocks; the starting time, however, varies by Time Zone. Here in New York the times are 10am-1pm and 3pm-6pm. Are you an early riser? You might try taking it in at the Pacific coast, where the times are 8am-11am and 1pm-4pm. Are you a night-owl? Then head over to Budapest, perhaps on the Budapest Semesters in Mathematics, where the “morning” session runs 4pm-7pm and the “afternoon” session 9pm-midnight!

Websites with the problems usually pop up shortly after the competition is completed; websites with the answers appear a few days later. We’ll post links to those sites in the Comments as we discover them. Previous problems and solutions can be found here.