The Math Competition

The lecture hall was completely packed, everyone sitting shoulder to shoulder, elbows bashing into elbows quickly followed by muttered apologies as we juggled pencils, clipboards, and calculators into a somewhat comfortable position. A supervisor stood at the podium, reciting rules that we had heard so often we could almost state them from memory. We were only half-listening, shifting impatiently as we waited for the proctors to pass the packets and scratch paper down hundreds of rows to a thousand people. We had trained for this all year, sitting in sweltering classrooms with our noses half an inch from our papers, one hand typing madly into the calculator and the other scribbling furiously. Everyone else was outside enjoying the changing of the leaves, then the beauty of the snow, then the magic of life returning, fresh and new; for us, the arrival of the budding leaves and blossoms meant one thing: the State Competition was upon us. It was here that we tested whether or not we had learned enough, trained enough, to be the best team in the state. It was for this that we had worked so hard, snubbing the seasons that had tried valiantly to capture our attention. We were ready. We wanted to “Begin.”

The rules were declared; the contest was out! I flipped it over and skimmed the first question:

It was beautiful.

Through my pencil flowed the pieces, numbers and variables spinning together to form equations, equations weaving in and out, coming together in new, unusual, wonderful ways, creating a new whole, a whole based entirely upon math, and logic, and truth. Twenty beautiful problems, works of art meant to be explored slowly, thoroughly, to be appreciated fully, but we couldn’t linger. We were racing through the Louvre, past da Vincis and Picassos, pausing briefly only to glean what we needed before sprinting to the next work.

I longed to linger, to give these masterpieces the attention they deserved, but I had made a commitment to the team. “Bring home the biggest trophy,” Mr. Tee had said on the long bus ride here. We all laughed, but the competition this year was formidable, and being a freshman, thus a newcomer, was no excuse not to do well. I could not dillydally about a couple of problems while the time slipped away from me. Upon finding a solution, I reluctantly pried my eyes away from the contours of the problem, scribbling the answer down on the contest sheet and reading the next question:

Another masterpiece, its solution graceful, its beauty beckoning to me, tempting me to analyze its every twist and turn. My stomach squirmed as I tore my eyes away from it and moved on to the next problem.

And so it went, each question tantalizing in its elegance, each question seeming to exude offense as I denied it the attention it deserved, each question becoming more of a problem as they increased in intricacy. My pace slowed, and I found myself slipping slowly into number eleven, gliding along a tangent line that gently caressed a circle, following the radius to the center before leaping lithely to the center of another circle that lightly touched the first. It was such a simple, elegant solut—

“Fifteen minutes.”

What? No! There wasn’t enough time, not for half the contest, not even for half of half the contest! I had to hurry, had to pick up the clipboard that had clattered to the floor from my hands, had to ignore a thousand brief stares, had to scribble down my answer and scan the problems, had to type into my calculator, scribble, scan, type, scribble, scan. Skip thirteen, too long. Scan. Type. Scribble. An answer! (Is it right? Keep going, watch the time, why did I have to be so slow?) Scan. Skip it. Scan again. Sketch. Scribble. Type. Scribble. Wipe sweat from my brow. (Had it always been this hot? Maybe it increased exponentially, all these bodies giving off heat—No! Concentrate!) Write down an answer. Scan. Multiple choice! Scribble. Another answer. Repeat.

“Five minutes.”

Only fourteen answers. I would not reach twenty. Mentally cursing myself, the time, and my obsession that ran far too deep, I scanned eighteen. Seemed simple enough. Apply law of sines, law of cosines, some properties of circles, and add the two answers together. A mistype. Delete, type again. Scribble an answer.

“One minute.”

Not enough time to do another problem. Time to guess at answers and scribble them down. My watch ticked in my ear as I scribbled guesses on the answer sheet. Thirty seconds. Erase some illegible answers and write them somewhat neatly. Almost done.

“Time!”

Answer sheets, some crinkled, raised above heads, little pink and green and blue flags fluttering nervously in the air, heads craned up at them to check answers, though there was nothing we could do about them. I reluctantly raised my own (pink) in the air. A proctor took it from my hands, storing it out of sight, but not out of mind.

We were packed into another lecture hall, juggling nothing but our apprehensions and our bags. The room was dead silent, save for a proctor who was announcing the placement of each school for each competition.

“… And for freshman geometry: ninth place goes to…”

I cringed and clapped politely as she said the name of our school. Some people had gotten perfects, a couple of them from our school. With a whopping twenty two out of forty, I probably had gotten one of the lowest scores. Other than Geometry, though, our team had done very well, placing third in Algebra and Precalc, second in both Eight Persons, and first in Two Person and Calculator.

“And now, for overall placement.”

More proctors brought out the trophies. The lecture hall murmured. I heard a junior on our team whisper, “Why is the second place trophy bigger than the first?”

Taking a closer look, I saw that he was right. The first place trophy, though a considerable three feet high, was eclipsed by the second place trophy, which was almost as tall as the short proctor who placed it on the stage. The room became silent once again as the proctor announced who placed where.

“… Second place goes to…” he said the name of my high school. Laughter and clapping rang from our section, and a thousand eyes once again glanced in our direction, this time in confusion.

“We’ll do better next time,” I heard a friend shout over the din. He was right. I had three more years. I had time to improve, to practice focusing on finding an answer during the contest, to appreciate the beauty of Math after the contest was over. We had time to finally get first place. In the meantime, we had done as Mr. Tee had asked. We did bring home the biggest trophy.

Author's Note:

The questions featured above are real questions for the ICTM Math Competition. I do not remember which year they are from— only that they were questions for at least one of a past year’s Geometry tests.