At the next math practice, Saeon went to the gallery. They passed the arch where Saeon had finished in their own words. Today's divided boards waited in the next space.
“I'll look at this one.”
Dure spoke before opening the notebook. Saeon looked down at the triangular folding board. The words Saeon wanted to put down first weren't written yet.
Last time in science, Saeon had redrawn the pictures. That hand had put a guess ahead of the record. Today, too, it seemed ready to arrive before Saeon's feet.
Floor 1 · Class F
Puzzle Gallery · Divided Boards
The navy stone table came into view, with its eight corners. All three silver trays were empty. The blue cores had been put away.
The three little lamps at the edge were dark. Two plastic boards lay in the middle. Both were long rectangles of the same size.
Their corners were rounded, and their surfaces weren't shiny. Each had three blunt dividers. This time, the dividers were fixed in place.
All four parts were equally wide and equally tall. They filled each board without gaps. On the left board, the first two parts from the left were teal.
On the right board, the first three parts from the left were teal. The rest kept the pale background color. The color lay flat on the boards.
Each board had a small label space below it. Both spaces were still empty. This was where they would put fraction labels for the gallery.
Saeon opened the folding board on the shelf beside the table. Last time's one fourth was on the back. This time, more parts were colored.
“We'll finish this one fast, too, right?”
Saeon's hand reached toward the labels. Sodam set the piece box farther back on the shelf.
“Hang on. We haven't looked yet.”
The hand stopped over an empty label. Sodam's eyes moved between the two boards. Dure set down the notebook and opened a hand before them, too.
“Oh. Your thoughts first.”
Saeon brought the hand back to the shelf. That didn't mean they had to put off starting. Saeon could write down the first things they noticed, then show the others.
Beyond the table stood the closed door to the next floor. The wide space before it was clear. The hallway behind the friends stayed open, too.
Saeon looked down at the boards again. Hands here had to come before feet heading to that door. Saeon wanted to fill those empty labels.
Dull amber knots of light wrapped around the two boards. Cream-colored eye-like gaps appeared inside the rounded shapes. A Tangle, made from a mistaken idea.
On the left, the bends in the strands were easy to see. On the right, a smooth layer circled the board. It looked so much like a neat rim that Saeon had to look again.
It didn't hide the teal spaces or the dividers. It didn't stretch beyond the boards. While Saeon's hand stayed back, the knots didn't grow.
Quest
Upside-Down Tangle
Four equal-sized parts in each board
What fraction of the right board is teal?
Reward: Skill Boost
Saeon tried writing the numbers, starting with the left. The whole had been divided into four parts. Two were colored.
Saeon wrote four, counted first, above a short line. Two went below it. For the right board, Saeon started with four again, then put three beneath it.
Left 4/2 · Right 4/3
Saeon stood the folding board in front of the two labels. The bottom numbers matched the teal spaces. The right board's rim looked neat, too. It all seemed finished.
“I wrote everything I counted.”
Saeon's hand stopped before sliding the folding board toward the labels. Dure's fingertip was following the edge of one board. It kept going past the end of the teal.
Did the whole end where the colored part ended?
Saeon didn't attach the folding board. One pale part remained on the right. Only at its far end did Dure's hand stop.
Sodam pointed to the gap between the two boards.
“Each board is one whole.”
Sodam pointed out the left board's end and the right board's end separately.
“All the way here. And all the way there.”
Saeon lined up the boards' bottom edges, leaving a gap between them. Now it was clear where each board started and ended.
An amber strand twitched at one edge. Saeon didn't move the dividers. The parts were already the same size.
Last time, they had needed to fix the widths. Today, the boards didn't need fixing. Saeon looked at the numbers above and below the lines.
“I could've called one part 4/1.”
The one fourth from before came back to mind. That time, four had gone under the line. Today, Saeon had put it on top just because it was counted first.
“I flipped the two and three this time, too.”
Saeon turned the folding board inward. The label spaces were still blank. Before copying the wrong words, Saeon wanted to fix the reason behind them.
Sodam pointed along the left board's upper edge. A fingertip moved the same distance between dividers. Along the bottom, it followed the gaps again.
“The whole is split into four equal parts.”
Sodam checked the right board separately.
“This one's the same. Equal heights, too.”
Saeon looked at two teal parts and two pale ones. Different colors. All the same size. The right board had four equal-sized parts, too.
“Four is how many parts the whole is split into.”
Saeon erased the numbers above and below the lines. The short lines stayed. Beneath each one, Saeon wrote 4 again.
Saeon held the folding board by the two label spaces. Following one board right to its end gave four parts. The counting didn't stop where the teal ended.
A thin cream-colored pin stretched from Sodam's fingertip to the right board's smooth strand. Sodam's hand stayed outside the board. Only the light touched it.
When the strand's shine stopped moving, the wrapped folds showed through. A Tangle had remained inside that neat-looking edge. Saeon still didn't set down the folding board.
Dure pointed to the teal spaces on the left. The fingertip moved from the first to the next. It didn't cross into the pale parts.
“Two here.”
Next came the teal spaces on the right. The fingertip passed over three parts, one at a time.
“Three there.”
Saeon wrote 2 above the left line. Above the right went 3. The hand about to copy them onto labels returned to the shelf.
Dure swept a fingertip along the notebook page's edge. Saeon waited until Dure looked up. This time, Saeon didn't start with done.
“Equal-sized parts. The chosen numbers match, too.”
Dure pointed between the boards and the written fractions.
“That's enough to finish.”
Saeon reread the corrected numbers. First came one whole left-hand board. A fingertip followed its two teal parts out of four equal parts.
“Two parts make two fourths.”
After looking all the way to the right board's end, Saeon read that one, too.
“Three parts make three fourths.”
Saeon copied 3/4 onto the right label and 2/4 onto the left. Each label went below its own board.
The bottom 4 told how many equal parts made the whole. The top 2 and 3 told how many of those parts were chosen. Saeon matched the written fractions to the boards again.
The dividers hadn't moved. The two teal parts and the three teal parts were just as they had been. What changed was the number on each label.
The last strands on both boards unraveled together. The amber knots scattered into cream-colored specks. The smooth false rim disappeared, too.
All three little lamps around the table came on. Saeon rested an empty hand on the shelf. The whole Dure had traced was now clear in the labels, too.
Quest Clear
Whole and chosen parts checked
Upside-Down Tangle · Unraveled
Skill Boost: “Equal Parts” — Fractions
“I listened to the end this time.”
Saeon turned the folding board a little toward Dure. Before closing the notebook, Dure looked at the corrected numbers.
“And I got to the end of my words.”
Sodam took a hand out of the gap between the boards. Saeon set the folding board on the shelf. The finished labels stayed below the boards.
A small recess opened at the front of the table. Saeon bent down, keeping both hands outside. Inside lay a real stone stair piece with three steps.
The small hollow above its top step was still empty. A little stone remained separate below. No letters or patterns appeared.
Blue light traveled down from the top to the little stone. After a moment, it climbed the step edges again. The two directions were the same as last time.
The stair piece lifted a little from the recess floor. This time, the light beneath it continued toward the floor outside. A thin line pointed toward the door to the next floor.
Saeon turned only their head to follow the light's end. The light lay low over the floor. The piece didn't move along that line.
“It's heading toward the door.”
Sodam and Dure watched from outside the recess, too. The little stone below stayed separate. Saeon didn't reach toward either piece.
The stair piece settled onto the recess floor. The little cover closed. The thin line of light on the floor faded away, too.
Saeon straightened and looked at the door. It was closed, just as before. Nothing had moved into the wide doorway space.
At first, Saeon had only wanted to fill the labels. Now Saeon knew what the bottom numbers meant, too. The hand had needed to wait until a friend's words reached the end.
Saeon folded the board and picked it up. Dure hugged the notebook, and Sodam gathered the piece box. They stepped away from the table into the open hall.
It was still the same floor at the bottom of the tower. Saeon pictured the light that had gone toward the door. The heights beyond it remained out of sight.
What was at the top?