The Chalk Square Outside Room Nine

Pria sits at the desk by the window in Room Nine. She stares at the first page of her maths exam. She is forty-three. She works nights at a warehouse, and she has studied for this paper every morning for a year. Her pencil case is on the desk. Her hands are cold.

The invigilator walks slowly between the rows. She is young, and her name badge says Lotte. She holds a stack of spare papers as if they might bite her. Pria guesses it is her first time.

"You may begin," says Lotte. Her voice cracks on the last word.

Pria begins. The first question is easy, and so is the second. By the fifth, she feels something she has not felt in a classroom for twenty years. She feels clever.

At twenty past seven, a small sound comes from the door. Lotte is whispering with a man in a grey suit. He has a lanyard and a tired face. He points towards the window, and then he leaves. Lotte comes back down the aisle with her eyes fixed on the floor.

She stops beside Pria's desk and bends down. "Sorry," she whispers. "I cannot talk during the exam. But could you look outside? Only look. I am not allowed to ask about the paper."

Pria frowns. Then she lifts her head and looks through the window.

Below, on the pavement outside the main door, a large drawing covers the paving stones. It is made of white chalk. Pria sees a square, and inside it a smaller grid of nine boxes. Each box holds a number, except the middle one. The middle one is empty.

The numbers are eight, one, six in the top row. Then three, blank, seven. Then four, nine, two.

Pria looks at it for a few seconds. Then she looks back at Lotte and nods once. She returns to her exam, because there is still a lot of paper left. But her mind keeps drifting down to the pavement.

For the next hour, the room is silent. Pria finishes question fourteen. She checks her working, and then she checks it again. At eight twenty, she turns over her last page and puts down her pencil. There are still thirty minutes left, and the rules say she must stay in her seat.

So she sits and looks out of the window. The pavement drawing is clearer from up here. Whoever made it drew each line with great care. The digits are neat.

She does the sum without trying. Eight plus one plus six is fifteen. The first column adds up to fifteen as well. Every row, every column and both diagonals should be fifteen. It is a magic square, and the missing number is five.

At eight fifty, a bell rings. The students stand, stretch and hand in their papers. Lotte collects them one by one, and she counts each pile twice. When Pria gives hers over, Lotte holds on to it a moment too long.

"Thank you," Lotte says quietly. "Please wait outside the door. I need to ask you something."

In the corridor, Pria leans against the wall. Her legs feel weak. She has finished. Whatever the result, she has finished.

Lotte comes out two minutes later with her bag. Her face looks pale.

"I am so sorry," she says. "You have just done a two-hour exam, and now I want a favour."

"What is the problem?" asks Pria.

"The head of department thinks the drawing is a code." Lotte talks fast. "He thinks someone is signalling answers to the students. Or it is a joke about the exam. He wants to know who did it before the results go out. He wants me to find out." She lowers her voice. "I teach history. I do not understand any of it."

Pria almost laughs. "It is not a code," she says. "It is a magic square. The missing number is five."

"How do you know that?"

"Every row adds up to fifteen. Look." Pria takes a pen from her pocket and writes the numbers on her hand. "Eight, one, six. Three, five, seven. Four, nine, two. Fifteen, fifteen, fifteen. It is an old puzzle. Children learn it at school."

Lotte stares at the numbers. Then she lets out a long breath. "So it is harmless."

"It is harmless," says Pria. "But somebody still drew it, and I would like to know who."

They walk down the stairs together. The lobby is full of tired students and the smell of floor polish. At the main door, Pria stops, because the drawing looks different from ground level. There is something she did not see from above. At the bottom corner of the square, a tiny arrow points to the left.

They follow it. On the next paving stone, there is a second drawing. It is a small spiral with numbers along its curve. It is a different puzzle, and it is also unfinished.

"There are more," whispers Lotte.

The arrows lead them along the building wall, round the corner and towards the bins. Each stone holds a new puzzle. There is a triangle of numbers and a clock face with no hands. There is a little ladder with missing steps. Pria feels like a girl again.

At the end of the path, a man in a blue overall is kneeling beside the back door. He holds a stub of chalk and draws a careful curve. A bucket and a mop stand beside him.

"Good evening," says Pria.

The man looks up and does not seem surprised. He is about sixty, and he has chalk dust on his knees. "Good evening," he says. "Are you here for the next one?"

"The next one?" asks Lotte.

"I draw one every night during exam week," he says. "The students come out of the building looking so serious. I thought they might like something to solve on the way home." He glances at Lotte's badge. "I hope I have not made trouble."

Lotte opens her mouth and closes it again. "My head of department thought you were sending hidden messages."

"Only the messages that say, think about this," says the man, and he smiles.

Pria crouches beside him and studies the half-finished curve. "You were a teacher once," she says.

"I taught maths for thirty years," he answers. "Then my knees got old, and now I mop floors. But I miss it every day." He taps the paving stone. "This one is hard. Nobody has solved the first half yet."

Pria takes the chalk. She thinks for a moment. Her exam is finished, her shift starts in two hours, and she should go home and sleep. But the puzzle looks at her like a door that has been left open.

"Seven," she says at last, and she writes it in the gap.

The man leans closer. He reads the numbers and then reads them again. His eyebrows go up. "That is right," he says. "That is exactly right. Most people never see it."

Lotte lets out a small laugh. She sits down on the kerb, holds her bag in her lap and looks at both of them. The day has been very long for her.

"So what do I tell my head of department?" she asks.

"Tell him the truth," says Pria. "A caretaker drew a puzzle, and a student solved it."

"He will want a name," says Lotte.

"My name is not important," the man says. He picks up his bucket. Then he looks at Pria, and there is a bright, curious light in his eyes. "But I am running out of easy puzzles. Do you know any hard ones?"