Six Strangers

The party had six kids in it and four of them were strangers to each other, and the rain was not going to stop.

Maya had invited her cousin Devi, and Devi had brought a friend named Os, and Soren was there because Soren was always there, and two girls from the swim team stood by the window not talking to anyone. Six kids. A cake nobody was allowed to cut yet. And rain coming down so hard the gutter outside sounded like a drum.

Soren had his notebook open on the carpet.

"I'm mapping it," he said. "Who already knows who."

Maya dropped down next to him. "Why."

"Because it's awkward and I want to know how awkward." He drew six dots in a ring and wrote a name by each. "If two people already know each other, I draw a red line between their dots. If they're strangers, blue."

"That's a lot of lines."

"Fifteen," Soren said. "Every dot connects to five others. Fifteen lines total."

Maya started calling out pairs. Maya and Devi, cousins, red. Maya and Soren, red. Devi and Os, red. The two swim girls knew each other, red. But Os and the swim girls? Strangers. Blue. Soren and Devi, strangers until ten minutes ago, blue.

They filled it in, line by line, the rain keeping time.

When they finished, the drawing was a tangle of red and blue threads crossing the middle of the ring.

"Look," Maya said. She put her finger on three dots. "Me, Devi, Os. All red. We all know each other."

"A red triangle," Soren said.

Maya sat back. Something was tugging at her, the way it did before she had words for it.

"Do it again," she said. "Different people. Make it so there's no triangle."

Soren tilted his head. "What do you mean?"

"I mean color the lines however you want. Six dots. Try to make it so there's never three people all connected the same color. No red triangle. No blue triangle. Can you?"

He liked that. He flipped to a clean page and drew six fresh dots.

He tried.

He made one dot all red to its five neighbors. Then he had to be careful, because any two of those red neighbors, if they were red to each other, made a red triangle. So he colored them blue to each other. But there were five of them, and five dots all blue to each other meant blue triangles everywhere.

He crossed it out. Tried again. Mixed it up. Three red, two blue from the first dot. Worked outward, fixing one, breaking another. A blue triangle would appear in the corner. He'd recolor a line to kill it, and a red triangle would open up across the page like something surfacing.

The swim girls drifted over to watch. Os crouched down.

"Just leave a line out," Os said.

"Can't," Soren said. "Every pair is either acquaintances or strangers. There's no blank. Every line gets a color."

He filled three more pages. Maya watched his pencil instead of the drawings, watched where it hesitated.

"You keep getting stuck in the same place," she said.

"I know."

"Like the triangle's already there and you're just choosing which color."

Soren stopped.

He looked at the half-finished page, four dots colored, two to go, and a red triangle and a blue triangle both waiting in the gaps depending on what he did next. He set the pencil down.

"Pick any one dot," he said slowly. "It has five lines going out. Five lines, two colors."

"So at least three of them are the same color," Maya said. "You can't split five into two piles and keep both piles small. One pile's got three."

"Three lines, same color. Say red." Soren's voice picked up speed. "Going to three other dots. Now look at just those three dots."

Maya leaned in. "If any two of them are red to each other, that's a red triangle, with the first dot."

"And if none of them are red to each other," Soren said, "then all three are blue to each other."

"Blue triangle." Maya breathed out. "There's no third option. You're trapped either way."

They both stared at the page.

"It doesn't matter how you color it," Soren said. "With six. It can't be avoided."

"Try five," Maya said suddenly.

He drew five dots. And with five, it worked. A red pentagon around the outside, blue lines crossing the middle in a star. No triangle anywhere. Clean.

"Five is fine," Soren said, and his hand was not quite steady. "Five you can dodge it forever. Six you can't. One person. One extra person changes everything."

Maya looked up from the carpet at the six of them. The cousins. The swim girls. Os. Herself. Six people pulled into one room by rain, half of them strangers an hour ago.

"So in this room," she said, "right now, no matter who knows who, there's three of us who all know each other, or three of us who are all strangers. Has to be. Even if we'd never met before today."

"It was true before we drew it," Soren said. "It was true the second the sixth person walked in."

Os frowned at the pentagon. "That's just these six. What about a whole school?"

"Bigger," Soren said. " "

Maya didn't say anything for a second.

She had spent a lot of her life feeling like the extra person. The one who came with someone, who didn't quite fit the shape of the room. The sixth dot.

"The order doesn't show up until the sixth one," she said. "You need the one that doesn't belong yet. That's the one that forces it."

Soren wrote the number six in his notebook and circled it twice.

"What's the number for a school," Maya asked. "For four hundred people. The biggest guaranteed pattern."

"I don't know," Soren said.

"Does anybody?"

He looked up. "For a lot of them, no. Nobody knows. They've proved the patterns are in there. They can't find out how big they get."

The rain was still falling.

Maya stood and walked to the window where the two swim girls had been strangers an hour ago, and she pressed her hand flat against the cold glass, and started counting the people she could see through the rain.