Fred Roggin (FR): Is the glass half full or half empty when it comes to test results for California students? According to the lasted data, test scores are up in math and English, but not by much. Nonetheless, at least they are inching upwards.

When it comes to the cream of the crop, four California high students proved to be the best in the world in math.

Joining us are Julia Huang a sophomore from Lynbrook High in Saratoga and Rebecca Burks, a junior from Danaidae Learning Studio in Los Altos. Both won medals in the Girls Mathematical Olympiad in China.

Girls, congratulations! Thanks for being here.

Rebecca Burks (RB): Thanks.
Julia Huang (JH): Thanks.

FR: All right, Julia, I’m going to start with you. Why do you have a love for math?

JH: I guess I just love playing with numbers.

FR: And, obviously you played with them quite nicely when you were in China. I know the test was two days long, four hours a day, and you only had four questions. Rebecca, that seems pretty simple to me.

RB: Well, each of the questions was pretty difficult.

FR: How long did it take for each question?

RB: They give you about an hour for each question, but generally it takes longer than that so you don’t have time to get to all of them.

FR: Okay. Well we want to see exactly how adept you are at mathematics. Julia, I have a question for you. Are you ready?

JH: Okay.

FR: Do there exist positive integers m; n, such that m²⁰ + 11ⁿ is a square number?

JH: No.

FR: No, and why would you say that?

JH: Well, this problem was on the test. This is actually the first one I looked at on the second day. And then I first considered using modulos for 4, 6, 8, and 9. I tried a bunch of random stuff and then I figured out using modulo 11 that it was impossible.

FR: And, I would have used modulos as well. So I think you made a wise choice there. Now Rebecca, let’s see if you can get this one.

A tennis tournament has n > 2 players and any two players play one game against each other (ties are not allowed). After the game these players can be arranged in a circle, such that for any three players A;B;C, if A;B are adjacent on the circle, then at least one of A;B won against C. Find all possible values for n.

RB: You start by looking at how. I drew a graph of the points. If one player won against another, I would draw an arrow from the winning player to the losing player so that the winning players would have the tail of the arrow. You do that in even numbers. If you have two points that are right across from each other and basically the arrows between those points have to go in both directions at once. So it can’t work. It cannot work.

FR: That’s right that was the correct answer. Now here’s a question for both of you. Are you ready? And either one of you can answer when you have the answer. Let’s see who gets it. Tell me when you’re ready.

JH: Ready.
RB: Ready.

FR: Here we go. How much wood can a woodchuck chuck if a woodchuck could chuck wood? Go!

JH: A woodchuck could chuck…

FR: Correct, Julia! Good job! Well done! I’ll tell you something you’re both young and your futures are ahead of you and you are brilliant. Be proud of what you have done. Julia and Rebecca, congratulations again. And, thanks again for being with us.

JH: Thank you.
RB: Thank you.

NOTE: To see the televised segment, please go to the URL link at the top of this webpage.