Winning Ways for your Putnam Days
Daisy did not grow up around other gifted kids, and as a result grew up thinking she was as unique as a snowflake. She had planned to slay the Putnam the same way she murdered the SAT; instead, she got a zero, which, to be fair, is the most common score. The next most common is 1. Out of a hundred and twenty possible points. That’s why she enrolled in Putnam class, which met once a week.
There were fifteen students in the class and only one other girl, Guo-Lin, who scored a thirty last year. Her parents had the good sense to give her a Chinese name, so that she even appeared smart on paper. Daisy was a good name for a pretty girl, but not for a smart one, a point she tried to explain to her Mom.
“But you are both!” her mom replied.
“It’s hard to be taken seriously if your name ends in y. And I don’t even have a middle name to fall back on.”
She could have been Ehuang or Xiao-Tong. Instead she was Daisy Chang, a name that was only half Chinese, like Daisy herself.
Demetri got a ninety-nine last year; that made him the star of the Putnam class. This year, he was determined to break into the triple digits. A lot of the students in the class had been doing math competitions since they were kindergartners, the same way other kids worked beauty pageants or geography bees. These people made up the advanced groups and worked on the hard problems.
Daisy was in the beginner group, which was sometimes referred to as the Zeroes and Ones.
She was joined in the group by Doug, who wore trendy glasses and untrendy clothes. He had statement buttons pinned to his backpack (for example: “There are 10 types of people in the world. Those who understand binary … and those who don’t.” which, okay, even Daisy had to admit was kind of funny even though she generally didn’t find Doug amusing).
The other member of Daisy’s group was Clay, who was slightly smarter than Doug and significantly more handsome. The latter point is somewhat negated by the presence of a girlfriend, an (ouch) art history major who would sometimes meet him after class.
“You’re cuter,” said Tilde confidently, after squinting at a thumbnail-sized picture of the girlfriend on Facebook. Tilde was Daisy’s best and only friend, and her opinion could be trusted on all matters relating to appearance.
“I thought so,” replied Daisy.
That meant Clay was not out of her league, which made him difficult to talk to, despite the girlfriend, so Daisy spoke even less to him than she did to Doug. Both boys did their best to coax her out of her shell, nominating her one afternoon to present a solution to the whole class.
She stumbled and stammered her way through a proof by strong induction, eventually showing that the nth term of the sequence in question was indeed an integer, thus solving A3 from 1998, and after she wrote her QED, both Doug and Clay shot up from their seats to give her a standing ovation. Such a gesture would have seemed condescending coming from any of her other classmates, but coming from her fellow Zeroes and Ones, it was unquestionably sincere.
Despite her studying, she only scored a 1 that year. So she tried again the next year, her third chance of four possible and still well below the maximum qualifying age of 25. By then Clay had dropped out of Putnam class, discouraged by his second zero in a row. Doug stuck around, buoyed by the 10 he got for correctly answering A1. That earned him a promotion to the intermediate group, though he would frequently stop by the Zeros and Ones every now and then to offer Daisy his opinion about last night’s episode of Mythbusters.
Daisy now had an entirely new group with a brand new girl, Terry, who was petite and frantic. And a little bossy, though Daisy was getting to be this way too. It was a consequence of being surrounded by girlfriendless boys, who would follow orders if it meant getting to talk to you. The third member of the group was Igor, who wore sunglasses to class. Trying too hard to be cool, Daisy thought as she rolled her eyes. She was cold to him to punish his vanity.
Actually, Igor was going blind and wore the sunglasses to protect what was left of his vision. Daisy tried to correct her initial misjudgment by being extra nice, and found Igor easy to talk to. His blindness resolved the tricky issue of eye contact during conversation, something that Daisy had always struggled with.
For their first date, they went to a jazz club that served sushi, which seemed unnecessarily challenging, but then Igor explained that he was trying to fit in as much chopsticks practice possible before he completely lost his vision. As he was not yet completely blind, that wouldn’t happen for another few years; he could compliment Daisy on her prettiness with credibility.
It’s not ideal to wear makeup when you’re dating a blind guy; you’ll smear his hand with paint. Perfume is the better choice, so Daisy asked Tilde to help her find an alluring scent.
The walls of the fragrance store were lined with elegant bottles, all fit for a magic potion. Tilde only wore scents that smelled like things you could eat, like angel food cake or pineapples, and tried to convert Daisy. But a dessert scent seemed like a poor choice for someone with a really good sense of smell, who would really understand the difference between a cupcake and cupcake perfume. Better to settle on something sophisticated, but not too strong. Something with fig or anise or Egyptian balsam.
First kiss. First boyfriend. These are accomplishments, though not the kind they give out plaques for. This wasn’t how Daisy imagined herself as a grownup. She thought she would be forever lonely with only a treasure chest full of math awards to keep her company. But her chest was empty and her heart was full.
In October she smelled like vetiver and listened to Charlie Parker. In November she cried during her topology midterm, after completely blanking on how to do Lebesgue integration. The tears did help her remember, and she earned a B+ on the test, a grade that seemed better and better as college wore on.
The Putnam was in December, and it was administered on the tenth floor of Evans Hall, which had great views before the suicide barrier was installed. Daisy sat at the back of the room, so as to be viewed by a minimum of people if a math meltdown were to ensue. This was her year, she was certain. This was her moment, and her past failures would make her eventual triumph so much more satisfying. That’s why she had to fail first. She understood now.
Of course the definition of victory had changed. First she wanted the Elizabeth Putnam prize, given to the highest scoring women. The next year she convinced herself to be content with a certificate of recognition, which was printed on parchment made to look old. This year she was aiming for fifty, a score that came with no prize, not even a mug or a temporary tattoo.
She looked over the exam booklet and her heart sank. She read all the problems and read them all again, and then copied them down word for word just so she could be writing something, so her despair would be less obvious as she considered what it would feel like to get another zero. To have her Putnam score be a binary sequence.
There were ninety-five people in the room with her, eighty starers and ten scribblers and five bright young people who were actually writing out solutions, hoping this year would be the year they were named fellow. Staring was not a winning strategy, it was a form of prayer really, the hope that if you sat perfectly still, gaze unmoving and concentration deep, the solution would decide you worthy and descend upon your pencil tip. Scribbling was the tactic of writing down any relevant information and hoping that the correct argument would leap forth from the mountain of evidence, like a needle glinting brightly from under a mound of hay.
She was hoping that by this point in her life she would be generating solutions, but genius still eluded her, so she settled for half-staring and half-scribbling. Maybe this year she’d get a two, if her scores were progressing arithmetically, or a three, if the sequence was instead exponential and given by the function 2x-1-1.
She read through the test one more time and decided that A2 was her last and best hope.
A2 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?
Daisy should be working on the first problem. Because that’s what you do, you start on A1. That’s the easiest problem on the test. But after reading through all six problems on the first part of the exam, A2 seemed to be her best shot at picking up any points.
She downsized the matrix, drawing a petite 3 by 3 over and over again and filling it in so that Alan would win, and then Barbara. It would do no good to consider a matrix with 2008 rows, 2008 columns and thus 4,032,064 entries, its magnitude would only choke you, better to take a small bite and chew it carefully. Take the whole three hours if need be.
She crowded her whole sheet of scratch paper with 3 by 3s, each filled with zeros and ones. The matrices began to look more and more like games of tic-tac-toe the smaller and smaller they got, and indeed this problem was an evolved take on the tic-tac-toe problem. There is no winning strategy for that game, but the player who goes second can always force a tie. And that’s the mathematical reason why tic-tac-toe isn’t fun.
The answer came to Daisy while she was staring and thinking about Alan and Barbara. How Barbara would be desperate to win, because it was her intellect at stake, not Alan’s. She was the one with something to prove, she was responsible for either demolishing a stereotype or maintaining it. And of course, she could never really demolish it. Victory would only grant her membership into the exception club. There she could join Guo-Lin, who sat at the front of the room, hunched over her test booklet, no doubt tackling A5 or A6 by now.
She considered that Barbara had to do better than Alan just to prove herself his equal. She could not win by copying him, she had to be smarter and prettier and more productive, a credit to her gender.
Except that in this case she could win by copying. She could separate the matrix into 1004 pairs of rows. And every time Alan wrote a number in one of the pairs of rows, she would write the same number in the same column of the other. That way she could force two rows to be identical, which would produce a zero-valued determinant.
She wrote the solution. Then she filled the rest of the test booklets with very formal looking nonsense, just in case she could pick up a single point for getting a good start on things. Then it was lunch.
Sandwiches were given out, choice of turkey or peanut butter and jelly. Daisy felt like a zombie, pacing, stumbling, holding her sandwich in one hand as she chewed and swallowed without tasting. She bumped into a couple of people before deciding to sit down and stay down until the half-hour break was over. Her throat ached from anxiety and silence.
“A1 was pretty easy, huh?” Doug again. Who either couldn’t or wouldn’t understand disinterest.
She stared at her sandwich. “No,” she said without looking up.
“Oh. Sorry. You’ll do better on part B.”
“Does anybody ever do better on part B?” It was Clay, who had returned to the Putnam after vowing not to. He missed the test, even though it treated him badly. Daisy hung onto his words with a single girl’s interest. The breakup with Igor had been mutual, but he had moved on so quickly that Daisy did feel as if she had been dumped. Her name was Marina and she was Russian like Igor, with curly hair that acted as blind-boy bait. Daisy would never have hair like that, no matter how hard she tried.
Clay had moved on too, and was now dating a sociology major. At least he was moving up in the world.
After the break was over, everyone returned to the test room for the B part of the exam. Daisy spent the next three hours grinding away at B1, but was never able to wear it down.
So that was it. A score of 10. Not even good enough to be mentioned in the department newsletter. Double digits, she told herself, squinting to staunch the hot tears that came welling up in her eyes as she walked home. Only the top third of contestants get a ten or higher. And that’s the top third of a really prestigious group of four-thousand undergraduates. Still the tears came.
You’re no longer a Zero or One, she told herself. You’ve left that group.
But the feeling remained. That terrible feeling of not being a genius. It threw the rest of her life out of focus. It was okay to be shy and quiet and have only one friend, to not care about clothes or makeup, as long you were smart. And she wasn’t, the Putnam said so.
She opted out of the test the next year to focus instead on grad school applications. Her GPA was higher than the department average, but low enough to put the top tier out of reach. She might make second tier. Minnesota. Davis. But not Princeton or MIT.
Of course she looked at the Putnam problems for that year, and even tried solving them. She got A1, though nothing else. That would have been another 10. She computed the regression line of all her scores, including the unofficial one. It predicted that if she took the test again, she would get a 15.
She was getting smarter, but slowly. She needed a brain growth spurt, but it wasn’t coming. Her head wasn’t built that way. It added knowledge slowly but permanently, and was not judicious about the type of information it collected. For instance, animal trivia tended to pile up, as did TV theme songs. Napoleon fish with their huge heads that grow bigger and bigger as they age. The Komodo dragons that could clone themselves. Here on Gilligan’s isle …
The acceptances came in the spring, in thick envelopes that brought no joy, only the feeling of being hopelessly average. She had aimed low and succeeded.
She didn’t matriculate anywhere. She couldn’t make herself. Instead she enrolled for a fifth year of college, now at the ripe old age of 20, and signed up for Putnam class for the last time. Her scholarship had run out—it was only good for four years—so she was paying for this herself. Her GPA had been steadily ticking up, and if her modeling was accurate, she might even get straight A’s this term.
Daisy took the Putnam one last time and got a 30. Nationwide, it earned her a rank of 166.5; the decimal accounts for ties, but it was the fourth highest score at Berkeley and earned her a mention in the department newsletter, where she was praised by her professors as being diligent and hardworking, modest and eager to learn. Absent was any mention of natural talent or innate ability. She was no longer gifted, not in this context. She had succeeded despite average intelligence, and was thus a role model for normal people everywhere. You too can be good at math if you spend your days bashing your head against it and your nights wondering why it doesn’t love you back.
She hoped the best times were ahead of her. And the things that had thus far eluded her might not be so far away. To be a math genius, to be fancy and lovely, to be sure of your place in the world and willing to take up more than your own share of personal space. There was always hope that these events would occur, a nonzero probability that fluctuated with the passage of time.
Dominica Phetteplace is a graduate of Clarion West Writer’s Workshop and holds a degree in Mathematics from UC Berkeley. Her work has appeared in Asimov’s Science Fiction, PANK, The Los Angeles Review, and Flytrap. Selected by Kamala Puligandla.
Image © Pete via Flickr Creative Commons.