At the next math session, Saeon walked half a step ahead. The navy stone table waited at the end of the wide hall. Same eight corners. Same silver rim.
In their first session, moving one core had switched on the lights. In the Experiment Area, Saeon had taken another look at a shiny cup. This time, the shares would be equal from the start.
Saeon stood at an empty tray. Sodam and Dure pulled theirs closer, too. The broad hall stayed open behind them.
A navy display appeared, its top-left corner shaped like little stairs.
Floor 1 · Class F
Puzzle Gallery · Next Math Session
Teacher Gwak set the cores in the middle. Round, blue-glowing spheres, all the same size. Three rows of five.
Saeon counted along each row with a fingertip. Not twelve this time.
“Fifteen cores. Equal shares for three people. None left over.”
Three trays. Three people to share with. The three small lamps around the edge were dark. Saeon looked from the nearest tray to both friends.
“There are two ways to do this one.”
Ichan's voice came from upstairs. Standing straight behind the railing, Ichan held up two fingers, then lowered the hand.
Saeon tipped up their chin. That second method promised on the first day came to mind. Today, they would find another.
“Then we'll find two, too.”
Saeon tapped the empty tray's edge. First, finish one method. This time, no tray would have more or less than the others.
“Three of us. So, three each.”
Saeon put one core on the nearest tray. The next went to Sodam, the next to Dure. One round, one core each.
Another round in the same order. Two on every tray. Without pausing, Saeon reached for the middle again.
One here. One for Sodam. One for Dure. Saeon put down the last core in that round and opened both hands. Three cores on each tray.
Saeon looked across them. No moving a core from one tray to another like on the first day. Equal from the start.
“See? All the same. Done.”
Saeon's hand went up. Sodam adjusted the glasses, looking past the trays.
“They're equal. But are we done?”
Saeon's hand froze.
Three on each tray. So why was the middle still blue?
Two rows of cores remained there. Three in each row. Six spheres, just like the ones on the trays.
A dull amber knot appeared on the right-hand lock. Two cream-colored gaps showed between its round, tangled strands. The same simple eye-like gaps as at the experiment bench.
Strands wrapped around the right tray's rim, too. A smooth amber shine covered it, as even and tidy as a job well done.
Saeon looked from that shine to the cores in the middle. Looking neat didn't mean everything had been shared. A cup's shine hadn't told the whole story, either.
The teacher pointed to the lock.
“It's a Tangle. A device made from a mistaken idea.”
The knot stayed wrapped around the two objects. It didn't hide the cores or reach toward the children. Even as Saeon watched, it stayed put.
Surprise Quest
Mixed-Up Places Tangle
Share every core. How many does each person get?
Reward: Skill Boost
Sodam pointed to the three trays, then moved a fingertip toward the middle.
“Equal shares. And none left over.”
Dure put a hand by the middle, too.
“Here. Six left.”
Saeon remembered saying three each because there were three of them. Three was the number of people getting cores. It didn't mean three cores for each person.
Saeon had used the same three for two different things. People outside the trays. Spheres inside them. Saeon pointed to each separately.
“Three was the number of people. Not each person's share.”
Saeon looked at the six remaining cores. The three on every tray could stay. The rest could go around in the same order.
“I'll keep going till the middle's empty.”
One core at a time, Saeon's hand moved from the nearest tray to Sodam's, then Dure's. One more round finished. Saeon drew back an empty hand.
Four on every tray now. Three still in the middle. Saeon remembered getting four in their first math session.
That had been the end then. Not today. These three in the middle belonged to today's set, too.
Saeon went around once more. One here, one for Sodam, one for Dure. With the last sphere set down, the blue glow in the middle was gone.
Five on every tray. Saeon checked both open hands, too. No cores left there.
“A recess opened.”
A shallow space appeared in the front rim. Keeping both hands outside, Saeon bent closer. The little stone stair piece from the first session lay inside.
Three steps with rounded corners. This time, Saeon could see beneath the lowest step. A small piece looked as if it could fit into the empty space there.
A line of light ran down and stopped at that spot. No letters or patterns. The edges of the gap stood clear at the end of the light.
Saeon raised a finger outside the recess.
“There's an empty spot underneath, too.”
Sodam pointed to it. Dure watched with hands drawn back. Nobody reached inside.
The piece at the experiment bench had a hollow in its top step. Here, there was a gap beneath the lowest step. Saeon pictured the two places side by side.
There was no sign of what belonged there. The place where the light stopped lingered in view, then the recess slowly closed.
Saeon straightened. The trays still held five each. The lamps were dark.
The amber shine peeled away from the right tray. Its silver rim showed again. A loosened knot remained on the lock.
“Five, five, five. We used them all.”
Saeon pointed to the trays and the empty middle. Sodam checked all three and nodded. Dure brushed a fingertip along the nearest tray's edge.
“Five each. None left.”
The last strand came undone. Cream-colored specks scattered upward and vanished. All fifteen blue cores stayed on the trays.
The three lamps lit together. The round latch on the lock moved smoothly, well away from the children's hands.
Fifteen shared equally among three people made five each. The amount one person got was their share. A short equation appeared beside the table.
15 ÷ 3 = 5
In the middle number, Saeon saw the three people. In the last number, the five cores on the nearest tray. Put all three shares together, and there would be fifteen again.
The teacher held an open palm toward them.
“Two methods. All three of you explain.”
Saeon glanced up at Ichan. They had followed the one-at-a-time method right to the end. Now to show that another route could reach the same place.
“This time, I'll start with two each.”
Saeon gathered every core into the middle. Sodam and Dure lined up the empty trays. The lamps stayed on.
Two on Saeon's tray. Two for Sodam. Two for Dure. After one round, nine remained in the middle.
Another round of two each. Four on every tray. Three left in the middle.
Saeon started to pick up two, then stopped. The number of remaining spheres matched the number of people. This time, Saeon could see where those three should go.
“One each for the last round.”
Saeon placed one on every tray. Five each. Empty middle. Exactly how the first method had ended.
“Two, two, then one. That's still five.”
Sodam pointed to the nearest tray and looked at the teacher.
“All three of us got the same number in each round.”
Dure spread a hand over the middle.
“Five each. We're done when the middle's empty.”
Saeon waited until both friends had finished. Beside Saeon's explanation, they had added the equal rounds and the place to check at the end. Those details completed the method.
Saeon looked across the three trays once more and drew back.
Quest Clear
Equal shares · None left over
One each per round, until the middle is empty
Mixed-Up Places Tangle · Unraveled
Skill Boost: “Fair Shares” — Division
“That makes two. See you at the move-up challenge.”
Ichan spoke from behind the railing. Saeon almost held up two fingers, then rested a hand lightly on the tray. The methods they'd found were right here on the table.
“Next time, three.”
Saeon turned to Sodam and Dure. Dure closed the notebook. They left the glowing table and walked into the wide hall.
Still the bottom floor. Saeon stopped and looked up, remembering the light that had halted beneath the little piece.
What was at the top?