Glassby

That sounds like a small detail. Glassby thinks it is one of the most important ideas in the whole lab, and one damp afternoon he finally got to prove it.

A group of young squirrels arrived at his bench arguing about a single word. They had been studying the other sort of solitaire, the classic kind, where a stack of cards starts face down and cards lie buried under others, out of sight. In their results, the solver sometimes marked a deal lost. The squirrels could not agree what lost meant. Did it mean the deal was truly impossible? Or had the solver simply been unlucky, choosing a path in the dark when a card it couldn't see would have saved it?

Glassby hoisted his magnifying glass like a banner. "Oh, this is a wonderful question," he said. "Let me show you two tables."

On the first table, he laid out a deal of the classic kind. Many cards lay face down, their backs a blank checkered pattern. "Here, you're making choices without seeing everything," he explained. "When you move a card, you don't know what it will uncover. So if a deal like this comes out lost, you have to be careful what you claim. Maybe there truly was no way through. Or maybe a different early choice would have uncovered exactly the right card, and nobody could have known it was there. You were playing partly blindfolded."

On the second table, he laid out a FreeCell deal. Here every card lay face up from the very start, all fifty-two of them spread across eight columns in plain view, with four empty free cells waiting in the corner as parking spaces. Glassby swept his lens slowly across the whole layout, and his cheeks swelled so round that one of the squirrels giggled.

"Now look," he said. "Nothing is hidden. Nothing at all. The solver can see every card, which means it can see every possible move and everything that move would lead to. It has the entire map. So suppose the solver searches every single path through this deal, every branch and every branch of every branch, and finds no way to win. What does that mean?"

The oldest squirrel spoke carefully. "It can't be bad luck," she said. "There's no hidden card that might have changed things. There's nothing left to discover."

"Exactly!" Glassby said, practically vibrating. "In a game with no hidden information, a fully searched loss isn't an opinion about how someone played. It's a proof. It proves that this deal, laid out exactly this way, can never be won by anyone, ever, no matter how clever they are. The loss isn't about the player. It's a fact about the deal itself, as solid as the fact that two plus two is four."

The squirrels were quiet for a while. It was a strange idea to hold: that a game could be so completely open that losing it became a certainty, the way a finished puzzle is a certainty.

"Does that happen often?" asked the youngest.

"Almost never," said Glassby, delighted. "With four free cells, nearly every FreeCell deal can be won. People who study the game have searched enormous collections of deals and found only a tiny handful that are truly impossible. So when the solver proves one, it's a little treasure. A deal the whole world could try forever and never beat."

Then Glassby did the thing that makes the lab trust him, even though he gets so excited. He lowered his magnifying glass and made his voice serious.