Tess Try-Small

"I'm Tess," she said, leaning her elbows on her knees. "I hate massive numbers. They are loud, and they like to boss people around. Whenever a problem tries to bully me with a hundred of something, I shrink it. I strip it down until it's tiny. Almost insultingly small."

"How small?" Min asked, looking up from his blank grid.

"What if there were only one light bulb?" Tess asked. "And only one person walking past?"

Theo frowned. "That's ridiculous. One person walks past one bulb and flips it on. The light stays on, and you're done."

"Congratulations," Tess said, snapping her fingers. "You aren't stuck anymore. You just started."

Theo rubbed his forehead. "That doesn't count. One light isn't the problem on the page."

"It's the start of the problem," Tess corrected. She tapped her pencil against the corner of her desk. "This move is called specializing—testing a huge, terrifying rule on the simplest example you can find. Big problems like to wear scary monster costumes. Inside, a hundred-light problem has the exact same bones as a three-light problem."

She gestured toward their blank scratch paper. "Try two lights and two people. What happens?"

Reet pulled the paper closer. "Person one turns both lights on. Person two flips switch number two, turning it off. So Light One is on, and Light Two is off."

"Now do three lights," Tess nudged.

Min dragged out a fresh sheet of grid paper. He drew three small squares and labeled them one, two, and three. "Person one turns all three on," Min said. "Person two flips number two off. Person three flips number three off. So Light One stays on, while Two and Three end up dark."

"Keep going," Tess urged, her heels tapping a steady rhythm against the workbench. "Don't guess. Just build it."

Anya leaned over the grid, her spirals completely forgotten. "Four lights," she murmured, tracing steps across the page. "Person one turns all four on. Person two flips two and four off. Person three flips three off. Person four flips four back on."

She stopped, her pencil point resting on switch number four.

"Wait," Anya said. "Light Four turned back on."

"List them," Theo said, taking the pen from Reet. "Which lights end up turned on?"

Min pointed down his neat column. "With one light, Light One stays on. With two lights, just Light One. With three lights, still just Light One. But with four lights, Light One and Light Four are both glowing."

"Do five lights," Reet insisted, his voice dropping to an excited whisper.

They worked together, passing the sheet back and forth. Person five flipped switch five off. Light Five ended up dark. They ran six lights, then seven, then eight, then nine.

"Stop," Anya whispered, grabbing the corner of the paper. "Look at nine."

Light Nine had been flipped on by Person 1, off by Person 3, and back on by Person 9.

"The lights that stay on," Theo read aloud from Min's chart. "One. Four. Nine."

The room went completely quiet, but the heavy, frozen weight was entirely gone. In its place was a sharp, clear energy.

"One times one is one," Reet said, his eyes wide. "Two times two is four. Three times three is nine."

"Square numbers," Min breathed. "Only the square numbers stay on."

"Why?" Theo asked, staring at the grid. Then his brain clicked into gear. "Because regular numbers have factors in pairs. Take six—its factors are one and six, two and three. Four factors mean four flips, so it ends up off. But square numbers have an odd number of factors. Nine has one, three, and nine—three flips total!"

Tess leaned back on her workbench, beaming as if they had pulled off a magic trick.

"There it is," she said softly. "You didn't need to simulate ten thousand switch flips. You just needed to listen to what the tiny cases whispered."