Lucy Zhang

CW: Eating Disorders

Eating Disorders as an Algorithms Problem Set  | Fiction |

Problem 1: Suppose n Hershey kisses are thrown into n glass jars independently and uniformly at random. For n ≥ 2, show that in expectation, a constant fraction of jars is empty.

There is one jar. The jar contains Hershey kisses–striped wrappers concealing white chocolate swirled with milk chocolate. When the guidance counselor asks if you’d like one, you say sure because saying no, thank you means sounding alarms. Twenty-two calories of sugar and fat dissolve in your mouth, a worthy sacrifice if it means nothing escalates beyond a heart-to-heart conversation and a promise to eat lunch.

Let there be two jars. There’s a chance one of them will be empty now. You close your eyes and choose, and when you pull out an empty hand, you have never felt such respite while being watched by the woman who sent cafeteria staff to report back on your lunch box containing an empty Tupperware box, untouched spoon and fork wrapped in a crinkled napkin–all assembled on the table as though a meal had taken place, and then returned to the Velcro-sealed, insulating compartments. You sit across your phantom lunch, flipping through bright yellow SAT vocabulary flashcards.

When n ≥ 2, there’s a chance you didn’t eat the Hershey kiss and nothing entered your bloodstream as glucose. In this case, you return home with a hollow stomach. You finish homework. You pace between assignments. You sip hot water.

When n ≥ 2, there’s a chance you ate the Hershey kiss. You think how delicious which is how you know you’ve committed some grave sin. Food invites food. You return home and pull three Einstein Bros. sesame seed bagels from the freezer and stack them one on top of another, a non-structurally sound cylindrical tower nearly hitting the roof of the microwave. It takes one minute for the top bagel to become soft and warm, another thirty seconds for the middle bagel to be evenly warmed up, and a final seventeen seconds for the last bagel to defrost. That is one minute and forty-seven seconds for you to fit in several iterations of jumping jacks, the final torture before reprieve. You chew and chew until soft dough condenses to glutinous pieces between your molars. When the third bagel is gone, your stomach grumbles. You reach back for the remaining three frozen bagels and place one on the glass rotating tray of the microwave. One more.

But you guess it doesn’t make much of a difference now. There is only one jar and you eat the Hershey kiss, claiming how studies distracted you from eating, how you didn’t realize when any of it started to happen, how you’ll try your best as you mentally deduct calories from tomorrow’s intake to account for today’s deviation, and you are all smiles because this is a test: if you decline the chocolate, you fail and if you accept the chocolate, you fail and the only way to win is to, from the very beginning, let the n Hershey kisses miss all n glass jars, leaving nothing but visual distortions from the glass’s lack of optical flatness. You can probably do it, with your terrible aim.


Problem 2: You have a knapsack of size 10. There is an object of size 3 with value 6, several years’ worth of lies and truths-by-omission, and an 88 on a level from 0 to 100 for the dread of having sex. The size and value of a 0 ≤ α ≤ 1 fraction of an object are α times its size and value respectively. Choose a set of objects that fit in the knapsack and maximizes total value.

You stash away the lunch money your parents give you in your cracked plastic yellow piggy bank. You walk from the library to the Chinese noodle restaurant, where you answer take-out phone calls and guide customers to tables–the kind of customer who refuses to sit by the entrance door and instead loiters around the counter telling you that they see an empty table so why can’t they sit, a shift from five pm to nine pm, an alibi for dinner. When you leave home to attend college, you fuel your body with Guayusa-based energy drinks and the occasional Quest bar purchased from the university’s convenience store.

Sometime during everything–writing pseudocode and planning for your first real job after graduation and the pipe dream of living by yourself–no roommate, no parents, no one to ask you what you’re doing when you start boiling cabbage at three AM, too hungry to fall asleep, you find a partner who seems to like you and you seem to like them. Sex comes sooner than anticipated: before you’ve been assigned your first project at work, before you’ve moved out of your temporary housing, an apartment pre-stocked by the housing contractor company with butter and spaghetti and milk and Cheerios, before you’ve registered that a relationship means not wandering like a zombie from room to room to charge a phone or put on socks, where you can go days without speaking a word.

Thicc is the last thing you’d like to be called while someone is sitting on your face and applying lubricant between your legs. When they say thicc, you think, oh a sagging lump of lard. Here are the other things you ponder while engaging in sexual intercourse: how do people develop foot fetishes? What is there to like about breasts–certainly not their monthly soreness, or the requirement to wear an additional article of clothing for structural support, or the texture because you can get the same soft fleshiness from any limb overflowing with adipose tissue?

Once upon a time, lying down on any surface–even a bed with a memory foam mattress–bruised your back and tailbone. You wouldn’t call it pretty, but it certainly wasn’t thicc.

Dump everything out of the knapsack. Someone will come along and pick up the pieces.



Lucy Zhang is a writer masquerading around as a software engineer. She watches anime and sleeps in on weekends like a normal human being. Her work has appeared in Atlas & Alice, Okay Donkey, Jellyfish Review, trampset, and elsewhere. She can be found at or on Twitter @Dango_Ramen.

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