Sodam's First Move.

At the next math practice, Saeon went to the gallery. Sodam and Dure came, too. Teacher Gwak Doeun stood beside the table.

Last science practice, they had studied magnets of the same color. Change the facing poles, and the movement changed, too. Today, Saeon first noticed blue light inside silver trays.

The eight-sided, dark blue stone table was just as before. Dure put the notebook on the shelf beside it. A wide hallway lay open behind them.

Saeon took half a step ahead to their tray. Round cores sat in rows. Five, five, and three.

“Thirteen again.”

Sodam's tray in the middle held two groups like that. A gap separated them. On each side were rows of five, five, and three.

Dure's tray on the right was empty. Three matching trays, holding different amounts. The middle of the table had no cores, either.

The teacher moved a hand away from the arranged cores. The three little lamps around the edge were off.

“Look at the equation first. How many altogether?”

Saeon looked from the equation to their tray. Here was the thirteen. They wanted another look at what the three was counting.

“I found one more way.”

Ichan spoke from upstairs, standing straight behind the railing with an open palm. The hand stayed inside the railing, too.

Saeon remembered the promise from last math practice. They looked up and answered quickly.

“All three of us will explain in our own words.”

Ichan lowered the hand and waited. Saeon turned back. Sodam was looking between the two groups in the middle.

“I want to look at everything before I start.”

Sodam's hand waited beside the tray. Saeon watched the fingertips, then looked at their own group. They had already counted thirteen. Maybe they just needed to add the next number.

Saeon pointed outside their group with one hand and held up three fingers on the other. Not one core moved.

“Thirteen plus three. Is that it? Sixteen.”

Those three fingers were outside the tray. Saeon started to lower them, then stopped. Blue rows still filled the middle tray.

Which cores were the three Saeon had just added?

Dure brought their fingertips together in front of the empty tray.

“One group has thirteen.”

Sodam's eyes crossed the gap in the middle, then returned to the tray's edge.

“Two trays have cores. Thirteen twice makes twenty-six?”

Sodam left the question hanging. The hand stayed still, too. Saeon looked at one group in the middle tray, then shifted their gaze.

There was another short row inside that same tray. Point to the tray once, and that part got skipped. Saeon folded the raised fingers.

Amber light gathered around the lock on the right. Cloudy strands formed a round knot no bigger than a tray.

Two cream-colored gaps between the strands looked like eyes. The outer strands wrapped around the lock. An inner layer covered the right lamp beside it.

That layer was a smooth amber coating. The lamp's round shape showed through, making it look lit. The left and front lamps were still dark.

“Two layers of tangled thinking.”

The teacher pointed to the wrapped objects.

“It's a device made from mistaken ideas. Explain them, and it comes undone.”

The strands stayed on the two objects. They did not cover the cores or reach toward the children. Saeon lowered their hands and watched. Nothing spread.

Saeon looked at Dure's empty tray. Moving the groups could make all three trays equal. But today's practice meant leaving the groups where they were.

Saeon's hands waited outside the tray. Sodam adjusted their glasses and lowered a hand, too. Nobody had started adding by groups yet.

Then the shallow recess at the front of the table opened. Dure looked inside, fingertips together. Saeon leaned forward a little.

Inside were three little stone steps. The slot shaped like one more step, just above the highest one, was filled with blue light. There was still no stone in it.

The empty space beneath the lowest step was visible, too. Just below it lay a separate little piece. Until now, that stone had stayed apart from the stairs.

“The bottom piece is glowing, too.”

At Dure's words, Saeon looked lower. The small stone glowed the same blue as the upper slot. Light pooled around its rounded corners.

Even with the glow, the gap remained. The little stone had not joined the empty place. Saeon kept their hands outside.

There were no letters or patterns. Nobody took out a piece. When the recess closed, Saeon looked back at the blue rows on the trays.

The lamps were still off. Seeing a glowing piece had not finished their counting. Saeon studied the two groups Sodam was watching.

Sodam's eyes paused on each side of the gap. This time, they did not start checking all over again from the left tray. A finger moved below the first group on Sodam's tray.

“I'll point first.”

Sodam tapped the silver edge. A tiny light in the front lamp flickered, then settled. The lamp did not come on yet.

First, Sodam pointed outside Saeon's group.

“Thirteen here.”

The fingertip moved below the first group in the middle tray.

“Add thirteen. Twenty-six.”

Saeon looked down at the three fingers they had raised. Sodam had not added a number of fingers. Sodam had added the entire group the hand pointed to.

Sodam's fingertip crossed the gap and stopped below the second group. This time, it did not turn back at the tray's edge.

“Add thirteen again. Thirty-nine.”

Sodam withdrew the hand and looked at the matching rows.

“Thirteen, twenty-six, thirty-nine.”

The outer strands loosened. Cream-colored specks came free from the lock. The inner layer still coated the right lamp.

Saeon looked at the place where Sodam had first paused. The hand had moved from there, and the counting had followed. It was different from checking everything alone before saying a word.

Sodam looked down at the trays again.

“I was going to count the trays with cores.”

Sodam pointed to the middle gap.

“But there are two groups here. Both have thirteen.”

Saeon checked the five, five, and three on both sides. They needed to add thirteen twice inside one tray. An empty tray could not count as a group of thirteen.

“The tray count and group count are different.”

Sodam moved a finger from Saeon's side to the middle.

“Thirteen in each. Three groups like that.”

Saeon opened the hand they had held up.

“I only added three cores after thirteen.”

But Saeon had not held three cores. In front of them were whole groups of thirteen. Saeon pointed to their tray, then the middle.

“Three was the number of groups. We have to add thirteen three times.”

A thin cream-colored pin came from Sodam's fingertip. It stretched over bare stone to the coating on the right lamp. Sodam's hand stayed far from the knot.

The pin did not cover any cores. When the smooth layer stopped moving, the strands beneath showed. The left and front lamps came on.

Dure swept a finger along the edge in front of the empty tray. It stopped on the side nearest Dure.

“We added all three groups.”

Dure pointed to the one group on the left and the two in the middle.

“Thirteen in each. No group left out. Finished.”

The final strand broke into cream-colored specks. The coating peeled off the right lamp. Clear light came on, and all three lamps shone.

The cores remained exactly where they had begun. Thirteen on the left. Twenty-six in the middle. The right tray and center of the table were empty.

Thirteen in each group. All three groups added. No group split or joined. Short equations appeared beside the table.

Multiplication showed the same number added several times. Now, in the three, Saeon saw groups instead of trays. Only two trays held cores, but there were three groups of thirteen.

“Thirty-nine altogether. We didn't move any cores.”

Saeon looked at the teacher.

“Sodam found the part we missed.”

Sodam looked up, too.

“I added the two middle groups separately. I pointed to one group and started.”

Dure lifted a hand from the edge.

“I finished when we'd added all three.”

The teacher waited until all three had spoken, then nodded.

“Nice and clear.”

“I've still got one more way.”

Ichan spoke from behind the railing. Saeon looked up. Keeping a hand open, Ichan continued.

“I'll show you at the move-up challenge.”

Sodam lowered the hand reaching for their glasses. Before Saeon could answer, Sodam looked up.

“At the next station, I'll try pointing first again.”

Dure collected the notebook. A broad arch stood beyond the table. When Sodam turned toward it, Saeon stepped alongside.

They walked into the open hallway. Still the lowest floor. Saeon looked at Sodam's empty hand and lowered their own.

Next time, Saeon's might not be the first hand to move. Saeon stopped and looked up. The little stone glowed, but the gap beneath the stairs remained.

What was at the top?