It was the day of the end-of-term move-up challenge. Saeon stood before the closed door to the next floor. Sodam and Dure arrived in the same doorway space.
Today's challenge was set in two areas on the same floor. The science area was visible beside the math area. Saeon turned toward the gallery table.
The light reaching toward the floor in the last math session came back to mind. In science, too, light had flowed beneath the piece. Ahead stood the door where they had always turned back.
“Our turn.”
Saeon opened the triangular folding board on the side shelf. The wide hallway stayed open behind them. Even here, they could step back and look again.
Floor 1 · Class F
Move-Up Challenge · Math Area
Teacher Gwak stood beside the table, keeping both hands lower than the boards.
“All three. In your own words.”
Saeon had heard that on the first day, too. Back then, Saeon had raised a hand first, alone. Today, Saeon left space for the others to put down their things.
Sodam set the piece box farther onto the shelf. The hand adjusting the glasses paused.
“Hang on. I'm ready, too.”
Dure opened a blank page in the honey-colored notebook. Before writing, Dure opened a palm toward the table.
“Here. I'll do it, too.”
Saeon slid the folding board a little aside. There was room for the notebook and piece box together. Now the middle of the table was easy to see.
It was the navy stone table with eight corners. Three silver trays stood empty. The blue cores had been put away.
The three lamps around the edge were still dark. Three long rectangular boards lay in the middle. All three whole boards were equally wide and equally tall.
The left board was divided into four equal-sized parts. Only the first on the left was teal. The others kept their pale background color.
The middle board also had four parts. Their widths went from narrow to wide and back to narrow. One narrow part at the far left was teal.
The right board's four parts were equal in size. The first three from the left were teal. Only the last remained pale.
The blunt dividers were fixed to the boards. Paper copies matching each part lay beside them. They could compare the parts without changing the original boards.
Saeon rested both hands on the shelf. The two boards with less teal caught their eye first. In the middle, too, it was one out of four.
Dull amber strands wrapped around the door to the next floor. Cream-colored eye-like gaps appeared in a round knot of light. A Gate Tangle, a device made from a mistaken idea.
Its long strands followed the whole door. They reached the divided boards and the papers for comparing. The boards' boundaries and teal parts stayed visible.
The knot in front of the door stayed where it was. Waiting didn't make it spread. With the open hall behind them, Saeon looked at the boards.
Quest
Gate Tangle · Uneven Pieces
Find the board whose teal part is 1/4 of that whole board.
Reward: Skill Boost
Saeon tried writing middle on the folding board. A fingertip counted the spaces between dividers. One teal part and three pale ones.
“This one's one out of four, too.”
Saeon slid the folding board below the middle board. A fingertip stopped over the narrowest part. One chosen part. Four parts altogether.
Sodam pointed between the boards.
“Hang on. How big is that one?”
Saeon didn't push the folding board farther. Beside the teal part was a wider one. Both were one part, but their widths were different.
Did counting one of each make them equal amounts?
Saeon drew both hands back onto the shelf. Last time, they had fixed the top and bottom numbers in a fraction. Today, Saeon had thought putting the numbers in the right places would be enough.
Dure traced the board's outer edge. The hand went past the teal, all the way to the right end.
“Here. Let's look at the board again.”
Saeon wanted to compare the whole boundaries first. A fingertip followed each board's lower edge. Their right ends stopped in the same place, too.
“I'll match up the wholes first.”
Saeon picked up two paper parts from the left board. One copied the teal part; the other, a pale part. Saeon lined up their bottom corners and laid one over the other.
Their heights and widths matched exactly. Saeon tried the remaining copies, one at a time. However the papers were switched, nothing stuck out.
“The left ones match when I stack them.”
The strands around the door gave a little twitch. Saeon put the papers beside the board again. As Saeon's hand lowered, Sodam opened the piece box.
Sodam took out a short strip of cloth with no writing. It matched the width of one left-hand part. The boards were all the same height.
Sodam placed one end of the strip at the first divider. The other end touched the next divider. The same strip fitted the neighboring part exactly, too.
Sodam moved it along to the last part. Saeon followed where the strip's end stopped. All four parts ended at the same distance.
Next, Sodam held it against the middle board's teal part. The strip stuck out beyond that part. At the wider part beside it, the strip was too short.
“Even with four parts, the sizes have to match.”
Sodam lifted the strip away and laid it beside the board. A fingertip checked the middle board's parts separately.
“This one isn't split into equal amounts.”
Saeon erased middle. The narrowest teal part got another look. It was smaller even than one part of the left board.
“I just counted spaces. This isn't one fourth.”
A thin cream-colored pin stretched from Sodam's fingertip. The amber strands around the door stopped moving. The bent folds inside the wide knot stood out clearly.
Sodam started to put the strip back, then lowered it. The strip went against each part of the right board, too. Those four parts were equal, just like the left board's.
“These sizes do match. Let's check the chosen parts, too.”
Dure pointed to the teal on the right. The fingertip passed the first part and went through the third. It stopped before the fourth.
“Three teal here.”
Saeon remembered the number on the last label. One whole split into four equal parts, with three chosen. The right board was three fourths.
Dure's hand returned to the left board. This time, it stopped at one teal part. The pale parts after it were the same size.
“Four equal parts. One teal.”
Dure swept a fingertip along the notebook page's edge. Saeon waited until Dure looked up. The folding board didn't slide forward first.
“Left. Done.”
Saeon wrote left on the folding board, then 1/4 beneath it. This time, the size of each part had been checked, too.
One part of a whole divided into four equal-sized parts. That fraction was read one fourth. Saeon lined up the folding board beside the chosen board.
Saeon looked up at the teacher.
“I matched the wholes, then stacked the paper parts.”
Saeon pointed to the narrow middle part, too.
“Just finding one out of four wasn't enough.”
Sodam held up the cloth strip.
“The heights match. The widths have to match for equal sizes, too.”
Sodam's hand followed the dividers on the left.
“The strip fitted all four places on this board.”
Dure pointed separately to the single teal part and the whole board.
“One of four equal parts. Once we've checked that, we're done.”
The teacher kept both hands lowered while they spoke. Saeon lowered the hand that had finished its turn, too. Dure's last words stayed clear before the table.
Three Spaces Connected
First Move → Condition Pin → Finish Line
The final strand loosened. The amber knot circling the door unraveled. Cream-colored specks scattered from the boards and the door's edge.
The table's three little lamps came on. A small recess opened at the front, too. Saeon bent down, keeping both hands outside.
The real stone stair piece floated a little above the recess floor. The little stone below it moved, too. By itself, the small stone attached to the empty underside.
The separate stones became one piece. Blue light climbed the step edges. As it returned beneath the piece, it continued toward the floor outside.
Following that light, the piece set off toward the left side of the doorway threshold. Saeon watched until it left the recess. The cover closed over the empty starting place.
“It moved this time.”
Saeon straightened. From here, the far side of the table hid the threshold's details. Saeon didn't reach or step after the piece.
Ichan turned from a station with the same problem. Those whole boards were the same size, too. A cloth strip and paper copies lay beside them.
“I solved it by matching a strip and stacking the parts.”
Ichan put away the folded strip and waited. Saeon looked at their paper copies and Sodam's strip.
“We used those two ways, too.”
Ichan nodded. They had found the same number of methods. Saeon looked again at the two places where the friends had compared parts.
Today, Saeon had reasons to add to Ichan's words. Saeon could explain what matched when the papers were stacked. And Saeon had seen where the strip stuck out.
Dure briefly opened the earlier records. Trays with equal shares. Equal groups. Clock disks. Beside those drawings, Saeon folded the board.
Earlier Activities
Fair Shares · Equal Groups · Minutes and Seconds checked
No more new problems appeared. The three friends put the papers and cloth strip farther onto the shelf. The chosen board and checked explanation remained on the table.
Quest Clear
Equal sizes and chosen parts checked
Skill Boost: “Equal Parts” — Fractions
Saeon glanced toward the science area. Unraveled strands lay straight across the observation boards. Their light stayed on those boards.
When Saeon looked back at the door, light spread wide. It climbed slowly along the edges. The door opened, and the same light continued through it.
From start to finish, it was one unbroken glow. Saeon's name appeared within it.
Growth
Saeon · First Move — Opened the first space for all three
Saeon looked down at the hand that had lined up the boards. Once, that hand had put down an answer and finished alone. Today, it had made room for friends to carry on.
Inside the same light, the name on the display changed.
Growth
Sodam · Condition Pin — Connected the conditions for all three
Sodam rested a hand over the packed-away strip. Their eyes also went to where the stacked papers had been. Sodam closed the piece box without taking anything out again.
The light continued as it faded above the door. Last came Dure's name.
Growth
Dure · Finish Line — Set the finish for all three
Dure recorded the left board in the notebook. Beside it were the reasons all three had checked. A fingertip swept the page's edge before Dure closed the book and hugged it.
After the Growth display vanished, a notice appeared. The teacher watched the three friends from beside the open door.
“Nice and clear.”
Move-Up Challenge · Passed
All three explained in their own words.
Door to the next floor: Open
Saeon looked at the wide stairs beyond the door. These were the stairs they had always looked up at from outside. This time, Saeon stepped through.
“Let's go up.”
Sodam stood alongside with the piece box. Dure followed, still holding the notebook close. The three walked together inside the railing.
The gallery and doorway stayed open behind them. On the first step, Saeon looked up. The blue light of the joined stones came back to mind.
Could these stairs lead to where the light returned? That was still only Saeon's guess. Ahead, the stairs continued upward.
What was at the top?