Knowsley

One grey afternoon, a young rabbit sat slumped in the grass beside a half-finished board. "I'm stuck," she said. "Nothing works. I'll have to guess."

Knowsley padded over and sat down next to her. He looked at the board for a long, quiet moment. Tap, tap, tap.

"Do you know what's special about League boards?" he asked.

She shook her head.

"Every League board is built to be no-guess," he said. "Before a board is ever given to you, it's checked. Starting from the free opening, the numbers can prove every safe square, one step at a time, all the way to the very end. Every board. No exceptions."

The rabbit frowned. "But I'm stuck right now."

"Then here's the thing," said Knowsley gently. "If the board is no-guess, and you're stuck, then being stuck can't mean you have to guess. It has to mean there's a proof on the board that you haven't spotted yet. The answer is there. It's just hiding."

That changed how the rabbit looked at the board. It wasn't a wall anymore. It was a puzzle with a guaranteed solution.

"So where is it?" she asked.

Tap, tap, tap. "Let's look for the trickier proofs," said Knowsley. "Sometimes one number alone can't prove anything. But two numbers, looked at together, can."

He pointed to a one and a two, sitting side by side. "Look. The one's hidden neighbours are also all neighbours of the two. The one says there's exactly one mine among its squares. The two has those same squares, plus one extra. The two needs two mines. One of them is already in the shared squares. So the other one..."

"...has to be in the extra square!" the rabbit said. "It's a mine!"

"It's a mine," Knowsley agreed, smiling. "Proven, with no guessing. Two numbers together did what neither could do alone."

She flagged it. That opened up a new safe square. And then another. And suddenly she wasn't stuck at all. The board unfolded, proof by proof, until it was completely clear.