The Route Everyone Wanted

Uncle Deen tossed the marker onto the counter and rubbed his eyes. "Twelve houses tomorrow. I want the shortest way. You two are the math geniuses. Figure it out while I do the register."

Maya looked at the map of dots he had drawn. Twelve little houses scattered across town, each with a number.

"Easy," she said. "You just try all the ways and pick the shortest."

"So try them," said Soren. He had his notebook open already.

"Start at the shop. Go to the closest house. Then the next closest." Maya traced with her finger. "There."

Soren followed her line. "That's not the shortest, though. Look. You went all the way out to house nine and then had to come back past seven to get eleven."

"So closest-first doesn't work."

"No."

"Fine." Maya wiped her palm across the board, smearing the line. "Then we do it properly. Every single order. All of them. Then we just look at which one won."

Soren clicked his pen. "How many is all of them?"

"First stop, twelve choices." Maya was already going. "Then eleven left. Then ten."

"So twelve times eleven times ten," said Soren, writing.

"Times nine, times eight, all the way down." Maya leaned over his shoulder. "Keep going."

He kept going. The number got long. It ran off the edge of the line and he started a new one.

"Four hundred and seventy nine million," he said. He looked at it. "And that's if we don't count the reverse routes as the same. About forty million if we're smart."

Maya stopped moving.

"For twelve houses," she said.

"For twelve houses."

She grabbed the marker and added one more dot. "Okay. Thirteen."

"Multiply by thirteen."

"Fourteen."

"Times fourteen." Soren's pen was moving fast now. "Maya, this doesn't grow. It explodes. Every house I add, I multiply the whole thing again."

"Do twenty," she said quietly.

"Twenty houses?"

"Do twenty."

He did twenty. He had to stack the multiplication down the whole page, and even then he stopped partway and just estimated the zeros.

"It's got eighteen zeros," he said. "Maybe nineteen."

"That's a lot of pizza."

"Maya." He set the pen down carefully, the way he did when he wanted to be exactly right. "There are around eighty zeros' worth of atoms in the whole universe. Everything. Every star."

"Okay, so twenty houses is way less than the universe."

"No, wait." He picked the pen back up. "I said that wrong. Do twenty on top of twenty. Sixty houses."

He wrote sixty and the number of routes underneath it, and this time neither of them said anything for a second because the number of zeros went past the atoms line. Past all of it.

"Sixty houses," Maya said. "There are more ways to deliver sixty pizzas than there are atoms in the universe."

"Way more."

"That's not real."

"It's completely real. It's just multiplying."

Maya sat down on the floor behind the counter. "So a computer," she said. "A really fast one. Checks a billion routes a second."

"For twenty houses, sure, done before lunch."

"For sixty."

Soren did the division in the margin. He checked it twice. "If it started when the universe started. It wouldn't be close to finished. It wouldn't be a speck of the way finished."

"That's not a hard problem," Maya said. "That's a wall."

Uncle Deen called from the back. "You got my route?"

"Working on it," Soren called back. He turned to Maya. "Here's the part I don't get. Nobody has ever found a fast way. Not a shortcut, not a trick, not a formula. Smartest people alive. They've been stuck on this exact thing for like seventy years."

Maya lifted her head. "Wait. Seventy years?"

"They can't prove there's no shortcut. And they can't find one. It's just sitting there. Open."

"So it's not that we're not smart enough at the pizza counter."

"It's that nobody is. Yet."

Maya stood back up.

"Soren. There's a question that everyone in the world wants the answer to. Every airline. Every delivery truck. Every phone finding you a route. All of them want the shortest way, and none of them can actually get it, they just get close, and the real answer is out there and nobody has ever touched it."

"Right."

"And it's this. This exact thing on my uncle's whiteboard."

"This exact thing."

She looked at the twelve dots. Then at the smear where her wrong line had been. The little houses did not look small anymore.

"How do the map apps do it, then," she said. "They give you a route in two seconds."

"They cheat." Soren almost smiled. "They don't find the shortest. They find a really good one, fast, and they don't promise it's the best. They can't. Nobody can."

"Every route I've ever taken," Maya said slowly. "Might not have been the shortest. There might have been a better one nobody found."

"For twelve stops, we could actually find the real best. Forty million is a lot but a computer eats that." Soren tapped the board. "So Deen's route, we can win. This one we can beat everybody."

Maya looked at him. "But only because it's twelve."

"Only because it's twelve."

Uncle Deen came out wiping his hands. "Well?"

Maya pointed at the whiteboard, at the twelve small houses. "We can give you the perfect one for tomorrow."

"Good. That's all I need."

"Add one more house and we still could," she said. "Add a hundred and nobody on Earth could. Not the biggest computer there is. Not if it ran forever."

Uncle Deen laughed, picked up his keys, and thought she was joking.

Maya turned back to the board. She uncapped the marker and started drawing a fifteenth dot, then a sixteenth, watching the empty space between the houses fill up with roads that no one had ever counted to the end of.