Lexington, MA - This has been a milestone week: I have embarked on something called a “diet” wherein food I normally eat in small portions (leafy vegetables, non-fat comestibles, etc.) is consumed in higher quantities than what I normally eat (anything in the “burger” family, or anything that can be wrapped in bacon).

This particular diet comes from the land of South Beach, where they apparently don’t drink alcohol, don’t eat potatoes, and don’t care that you can’t put balsamic vinegar in everything.

Perhaps it was my altered body chemistry that made me challenge Lexington teen Elizabeth Synge to a math-off in my office.

PDF: The math test

PDF: The test answers

She and her mother, Laura Yaker, accepted my challenge willingly. Perhaps she already researched her competition and was ready to take me on — she is, after all, no stranger to high-pressure math contests.

She entered her first math competition in sixth grade (Elizabeth will enter 11th grade at Boston University Academy this fall). Mom Laura remembers watching the National Spelling Bee on ESPN that year, and seeing her daughter get excited when, during the intermission, the MathCounts finals would air.

Elizabeth then tried a competition herself. She entered the AMC 8 (American Mathematics Competitions), then competed in the AMC 10 followed by the AIME, followed by other competitions that belong on an eye chart rather than graph paper. Eventually she earned a place at the national competition for MathCounts — twice. In the second year she finished seventh in the written competition — the highest-ranked girl in the country.

But MathCounts is only offered to middle-school students. And Elizabeth has bigger problems to solve.

This weekend she will travel to Xiamen for the 2009 China Girls Mathematical Olympiad, which will take place Aug. 12-16. She is one of seven girls representing the United States at the event.

PDF: A sample of the type of questions in the competition

To prepare, she spent much of this summer running up snow-capped mountains in Russia and working out in an old barn lifting heavy farm equipment. At least, that’s what I envisioned training math competitions to be like. But no, she informed me, they’re not like Rocky IV at all.

She actually visited the University of Nebraska at Lincoln for a few weeks in June, honing her skills in working mathematical proofs and word problems.

Word problems. This, I know a little something about.

My confidence brimming, I procured our tests. I found five word problems taken from an SAT test on the Internet, and printed the questions and answers without looking at the test itself. This took multiple tries, as I first clicked a Netflix ad and, later, an ad for an online game that I probably shouldn’t play at work.

“I must warn you,” I told her, “I haven’t done high school math in a while.”

“Neither have I,” she replied. She took calculus in sixth grade, and is now enrolled in a math program at Boston University.

Uh oh.

Deep breath for me. With tests in hand we began.

Furious scribbling wound its way up and down my test paper. Across my desk, I heard nothing.

Three minutes went by.

“All done,” said Elizabeth. I was still on the second question: Something about “let $ be defined for all nonzero integers.” For me, “$” is always a zero integer.

I handed her the answers while I finished my test. “There … they’re all right,” she said. Was that a smirk?

I finished my test a few minutes later, and guessed at the final answer. I got two right — my 17-year-old self would have shook his head in disgust. Beat by a girl.

Elizabeth was gracious in her win. She even seemed to enjoy it.

After competing in China, Elizabeth and some teammates will host a math workshop for some younger students. It’s a task she loves — after college and graduate school, she may go into teaching.

Lesson 1: Don’t go into a math test on an empty stomach.