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

It rolled across the Green and stopped on the step of the painted wagon. Two of the seven locks on the trunk were open now. The third one glinted under the lanterns.

The canvas roof had a neat patch, and a tiny hammer was sewn in thread beside the stitches.

"Tonight I'm watching every move," said Danya.

"Tonight I'm going to beat them," said Beto.

A performer in a sparkly jacket stepped up to the chalkboard. Her name was Missa.

"I need a volunteer with a big number," she said. "Four digits, any you like."

Mrs Patel came up and wrote 4725.

"Now mix the digits up," said Missa. "Any order."

Mrs Patel wrote 7452.

"Take the smaller from the bigger," said Missa, and she turned her back to the board.

Mrs Patel worked it out with chalk. 7452 take away 4725. "Two thousand, seven hundred and twenty-seven," she said quietly, so Missa couldn't hear.

"Circle any digit but a zero," said Missa. "Don't tell me which. Then read me the rest, in any order."

Mrs Patel circled one of the sevens. "Two, two, seven."

Missa tilted her head. "You hid a seven."

The crowd gasped. Mrs Patel laughed.

Beto marched up to the board. "My turn."

He wrote 1234. He mixed it into 4321. He took one from the other: 3087.

He grinned and circled the 0. "Eight, seven, three," he said.

Missa did not turn round. "You hid a zero," she said. "Or a nine. I can't tell which, and that's why I said any digit but a zero."

"That's cheating," said Beto.

"That's the rule," said Missa. "A hidden nothing and a hidden nine leave the same sum. Pick again."

Beto circled the 8. "Three, seven, nothing."

"An eight," said Missa.

Beto checked the board. Three and seven and nothing made ten. He had hidden an eight. He sat down on the grass, very puzzled, and did not say "cheating" again.

After the show, Danya found Marlow sitting on the wagon step, polishing a brass lantern.

"Is she reading their faces?" asked Danya.

"I will not tell you how," said Marlow. "But write down what you got. Every difference the crowd made tonight. Then add up the digits of each one."

Danya wrote them down.

2727. Two and seven and two and seven: eighteen.

2728. Three and nought and eight and seven: eighteen.

2729. Five and one and seven and five: eighteen.

"They all make eighteen," said Danya. "And eighteen is two nines."

"What do your answers have in common?" said Marlow.

Danya looked again. 2727 was nine times 303. They were all in the nine times table. Every single one.

Danya thought about it all night.

The next evening he stood at the chalkboard. "I'll do the Reveal," he said.

"When you mix up a number's digits," he said, "the digits still add up to the same thing. So the number and its mix have the same remainder when you share them into nines. Take one away from the other, and the remainders cancel out."

He wrote 7452 − 4725 = 2727 = 9 × 303.

"So the answer is always a multiple of nine," said Danya, "and its digits always add up to a multiple of nine too. If you hide one, Missa just adds up the rest and asks how far it is to the next nine."

"Eleven," said Beto, catching up. "Seven short of eighteen."

Missa bowed to Danya. The crowd clapped for both of them.

That night, the third lock on the trunk clicked open.

Back on the Green

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

At school, Beto wrote down his locker number, mixed up its digits, and took one from the other.

He added up the digits of the answer. Nine.