Echo Edie

Owen blinked.

"Oh," he said. "Um. Because the slowest person is going to be the bottleneck. So if you send them with someone fast, the fast person can come back with the flashlight. So the slow person crosses once with the fast person, and then the fast person handles the rest of the trips."

Echo Edie nodded.

"So your idea is: send the slowest person first, paired with a fast person, so the fast person can shuttle the rest."

"Yes."

"Now," Echo Edie said, turning to Bex. "What were you saying?"

Bex said, "I was saying the slowest person should go LAST, so they only cross once."

"And your reason?"

"Because every time they cross, the whole crossing takes as long as the slowest person. So we want to minimize how many times they're walking."

"So your idea is: keep the slowest person out of the boat as long as possible, because they slow everything down each trip."

"Yes."

Echo Edie nodded again.

"And Joon," she said. "What were you saying?"

"I said: what if two slow people went together?"

"Why?"

"Because if both slow people cross together, that's still just as fast as one slow person crossing, since they walk at the slow speed anyway. So you might be saving a trip."

"So your idea is: pair the slow people together to use the bottleneck once for two slow people."

"Yes."

Echo Edie looked at all four kids.

"You have three ideas," she said. "Owen's: send the slow with a fast for shuttling. Bex's: keep the slow out as long as possible. Joon's: pair the slow people. They might all be right. They might combine in a way none of you have noticed yet. Do you want to draw the problem out and try all three?"

The four kids stared at her.

"You... you remembered all of that," Sam said.

"Yes."

"Even Owen's? He said it first and we were about to move past it."

"Especially Owen's. The first idea is the one most likely to get lost. I tried to catch it before it disappeared."

She faded.

The four kids looked at each other.

"Okay," Bex said. "Let's try all three."

The kids worked for another half hour.

In the end, they figured out something none of them had thought of alone, but each had contributed a piece to. The answer used Owen's shuttling idea, but it modified the shuttling to handle Bex's keep-the-slowest-out rule, and it added Joon's pair-the-slow-people trick in the middle. The answer was seventeen minutes.

It was the smallest answer any of them had been able to find.

When Echo Edie reappeared, she said: "Tell me what each of you contributed."

The four of them looked at each other.

Joon said, "I had the pairing idea."

Owen said, "I had the shuttling idea."