Bevvy

The day Bevvy explained it to the whole field started with two young hares arguing. They had each played a board, and they were comparing how many clicks they had used.

"I cleared mine in forty clicks," said the first hare.

"I needed sixty," said the second, drooping. "So you're way better than me."

Bevvy zoomed over and hovered between them, wings a soft buzz. "Wait, wait! Did you play the same board?"

They hadn't. Bevvy landed on the first hare's board and started counting, one leg tapping.

"Here's how you find a board's number," she said. "Some squares have no mines near them at all. They're zeros. When you open a zero, it opens all the squares around it for free, and if any of those are zeros too, they keep opening, like a ripple spreading out. So a whole patch of empty squares opens with one click." She tapped the board. "This board has four of those empty patches. That's four clicks."

"Then," she went on, "there are numbers that no empty patch reaches. Each of those has to be opened by itself. One click each." She counted them carefully, buzzing from tile to tile. "This board has thirty-six of those. So the fewest clicks this board could ever need is four plus thirty-six. Forty. Its number is forty."

The first hare's ears went up. "Forty. That's exactly what I did!"

"You played it perfectly," said Bevvy. "Not one wasted click."

Then she flew to the second hare's board and counted again. Empty patches, lonely numbers, tap, tap, tap. This board was bigger and busier, with fewer empty patches to help. "This board's number is fifty-five," Bevvy announced. "It needs at least fifty-five clicks, no matter who plays it."

The second hare blinked. "So I used sixty on a board that needed at least fifty-five..."

"...and your friend used forty on a board that needed at least forty," said Bevvy. "You both did well. But you can't compare forty and sixty, because the boards weren't the same. Yours was simply a harder board. The number tells you how hard a board is before anyone plays it."