Cage

Next, he moved his small pliers to a three-square pen marked 6×. He tested number blocks in his palm, weighing the possibilities carefully. A combination of one, one, and six failed immediately because the ones repeated inside the pen. But two, three, and one multiplied to six without breaking a single grid boundary. He turned the polished wooden blocks over like a locksmith trying keys on a ring.

Cage had not learned this trade from a formal guidebook. He had learned it years ago during the spring storm that flooded the guild warehouse.

At fourteen, he was an apprentice keeping the supply grid in order. Rows of pine bins lined the walls, each holding a precise count of copper rivets and iron bolts. A sudden squall smashed through the glass skylight, sending muddy water down the walls and washing away half the paper shelf labels.

When the storm finally stopped, the warehouse was in complete disarray. All Cage had left were the inventory totals written on his dry oilskin clipboard. One line noted that Shelf Four held twelve items across three bins, with no two bins holding the same count. Another line showed that Shelf Seven held eight items across two bins, with one bin double the other.

The storage lids were rusted shut, so he could not look inside the bins to count the fittings. Nevertheless, those simple total numbers boxed the correct answers in completely.

Twelve items split across three unique bins allowed only a few mathematical combinations. Once he checked the physical shape of the shelf, only one combination actually fit the available space. He rebuilt the entire storeroom using targets and operations alone, without ever prying open a locked lid.

The old quartermaster stood in the doorway, staring at the restored bins in surprise. "You didn't guess those labels, son."

"I didn't have to," Cage said, wiping oil from his palms. "The totals told me. A target plus an operation is almost a label already. You just have to listen to it."

Ada brought him into the Guild three years later for that exact ear.

"Everyone can fill a cage that has ten possible answers," Ada told him during his first interview. "I want the person who finds the cage that has only one answer, and starts there."

That habit guided everything Cage built. He always hunted for the tightest arithmetic cage first—the pen where the target, the operation, and the enclosure size left the fewest possibilities.

A single-square pen marked 7 was a free gift, holding a seven and nothing else. A two-square pen marked 1÷ was more subtle. The two numbers had to divide to one, which meant they had to be equal. However, the grid's main rule banned identical numbers in the same line, meaning those two squares could never share a row or column.

He read the fence, the plaque, and the grid's overall layout together. Where all three rules agreed, there was usually only one valid arrangement left standing.

"You are using two rulebooks at once," a visiting artisan complained one afternoon.

"Three, if you count the grid," Cage said cheerfully. "More rules, fewer answers. That's the trade. I'll take it every time."

By late afternoon, Maya was stuck on a three-square pen shaped like an elbow. The plaque on the corner read 12×.

"It could be lots of things," she said, tapping her chin with a pencil. "Two, six, and one; three, four, and one; or two, two, and three."

"Two, two, and three repeats a two," Cage pointed out. "Does this pen bend through the same row?"

Maya leaned down to check the board. "Yeah, two of the squares sit in row three."

"Then those two squares cannot hold the same number," Cage said gently. "Which of your combinations survives that extra rule?"

Maya went quiet, shifting the wooden blocks across the grid. "Only three, four, and one works without putting duplicate numbers in the same row. And there is only one way to lay them out."

Two separate facts she already trusted—the target on the plaque and the row rule—had met and agreed on a single answer.

"That's it," Cage said. "You didn't pick it. The two rules picked it for you."

While resetting the outer frames near the courtyard doorway, Cage met Vega. She was busy drawing star boundaries on her own wooden grid board.

"Still locking your numbers in pens?" Vega asked, smiling dryly as she wiped chalk dust from her fingers.