The hammer rang once. A spark jumped off the anvil and did not go out. It waited. They followed.

It hopped to the edge of the Green and dropped into Fiddle's forge. The coals glowed red.

"A town has broken something," said Fiddle. "Try it and see."

Inkling had a tick-weight on her belt now. Beto had nothing yet. He wanted something.

The cart's bell rang once, and the wheels began to turn.

The cart rolled into Halvingford. A wide brown river ran right through the middle of the town.

There was a new wooden footbridge. It came out from the east bank. It came out from the west bank. But in the middle, the two ends did not meet. The east end stuck out past the west end, side by side, like two hands that missed a high five.

"We were told to build half," said the east crew.

"So were we," said the west crew.

The east crew had built eight planks out. The west crew had built six. Eight and six make fourteen.

Inkling looked at the two ends. She was sure.

"Saw a bit off both! I can name it," said Inkling. "Take one plank off each end and they will fit."

A beaver waddled up the bank with a rope over her shoulder.

"What is the whole?" said Bundle. "First the whole, then the parts."

"Seven and five would fit," said Inkling.

"Would seven and five be halves?" said Bundle.

Inkling stopped. Seven was more than five. That was not half and half. Her ears went pink. She had named it too soon again.

Bundle's rope had a knot tied every plank's length.

"Show me the whole bar," said Bundle. "Hold it all together and look."

Beto held one end on the east bank. Bundle swam the other end across to the west bank, the way beavers do. Then they counted the knots between them.

Twelve. The river was twelve planks wide.

"Fourteen built, twelve needed," said Beto. "Two too many."

A green gecko scrambled onto a stone and drew in the mud with his tail. He drew a long bar for the east span and a shorter bar for the west span, side by side.

"Look at the bit that sticks out!" said Jut. He sat right on the end of the long bar. "That's the difference, right there."

Eight is longer than six by two.

"One's longer by this much," said Jut, and wiggled.

An ant with a tiny saw came marching along the rope.

"Equal parts, or it isn't halves," said Sawyer. "Every piece the same."

She folded the twelve-knot rope end to end, so the two ends met. The fold landed exactly at the middle knot. Six knots on one side. Six knots on the other.

"Two equal pieces make halves," said Sawyer. "Same length, same length."

Half of twelve is six.

A soft gold moth landed on the end of the east span and folded her wings.

"This is the part we don't know," said Q. "I'll wait here."

"How much should each side change?" said Beto.

The west span was six. Six was half already. The east span was eight. Eight take away six is two.

"Now you know my number," said Q. "Two."

But the east crew folded their arms.

"We built more," they said. "We worked harder. Why should we take ours away? Saw the planks off and they're wasted."

Everybody went quiet. Nobody wanted to waste good wood.

Beto turned to Fiddle. "What do we do?"

"What does the wood tell you?" said Fiddle.

Beto knelt on the east span and looked closely. The planks were not nailed. Each one was held by two round wooden pegs.

"How does it work?" said Beto. He pulled one peg. It slid out. The plank lifted up, whole. Burned into the underside was a tiny hammer.

"Like the clock in Tickwell," said Inkling.

Beto took a stick and drew two bars in the mud, exactly the same length.

"Six and six make the whole twelve," said Beto. "That's halves. You didn't build wrong. You built two planks of railing."

The east crew looked at the bars for a long time. Then they lifted out two planks, whole. The two spans met in the middle with a soft knock. Inkling hammered in the last peg.

The two spare planks went up along the sides as a railing.

"Show me the whole bar," said Bundle, and smiled.

That night, Fiddle let them make an even-rule: a little brass ruler with a hinge in the middle, so it folded exactly in half. It went on Beto's belt.

"Push it, pull it, twist it, see," said Fiddle.

The cart's bell rang twice, and the road ran home.

The spark dimmed to a warm dot and settled back on the anvil. The Green was just the Green again.

Back on the Green

At home there was one apple and two of them: Beto and his little cousin. Beto cut it. One piece was bigger. His cousin's lip wobbled.

"Why is mine smaller?" she said.

"Because I didn't make halves," said Beto. He laid the pieces side by side, like Jut's bars, and cut a sliver off the big one. Now they matched.

Tell the story back to someone. Why couldn't they saw a plank off each end?