FreeCell Game #11982: Why the Impossible Deal Can't Be Won

FreeCell game #11982 is the only deal among the 32,000 in classic Microsoft FreeCell that cannot be won. No sequence of legal moves gets all 52 cards home: every line of play runs out of free space before the Aces can be dug out. Volunteers found it in the mid-1990s while trying to solve every deal, and since then a series of computer programs built to search every line of play have confirmed it.

Here is the full layout, what makes it so hopeless, and the small changes that would make it winnable.

The layout

Columns are numbered 1 to 8 from left to right. Row 1 is the top of each column, the cards dealt first and buried deepest, and the last card in each column is the one you can move first. Only the first four columns have a seventh card.

We generated this layout with the same shuffle that Microsoft FreeCell uses, which Poozee's FreeCell reproduces exactly.

Why it can't be won

The Aces are buried almost as deep as they can be

Three of the four Aces sit at the very top of their columns: A♥ in column 1, A♠ in column 2 and A♣ in column 4, each under six cards. The A♦ is in column 7 under four more. That makes 22 cards covering the Aces, close to the maximum possible of 24. According to Michael Keller's FreeCell FAQ, the average deal has about 11.

To start any foundation you have to dig through at least four cards, and to start the first three suits you need to clear most of three separate columns. With only four free cells, the cards you remove have nowhere to go.

But deep Aces alone aren't the reason

Buried Aces make a deal hard, but they don't make it impossible. Game #617, which has a reputation as a hard deal, has 20 cards covering its Aces and is solvable. Game #1941, which the FAQ nominates as the hardest winnable deal of the 32,000, has only 14. (We counted all three with Poozee's FreeCell engine.)

What sinks #11982 is which cards do the covering. Look at the layout and you'll see:

• Three Kings are among the cards covering Aces: K♦ and K♣ in column 1 and K♥ in column 7. A King can only move to a free cell or an empty column, so each one costs you free space.
• Low cards are stuck behind the Aces they need. The 2♣ is one of the cards covering the A♠ in column 2, and the 3♦, 3♥ and 3♠ each cover an Ace too. None of them can go home until the buried Aces are out, so they also end up in free cells.
• The 2♦ is buried as well, at the top of column 5 under five cards, so even if you free the A♦ first, the diamonds stop there.

Each Ace you dig for fills your free cells with cards that have nowhere else to go, and there is never enough space left to reach the next one.

Our solver checked every position

Poozee's FreeCell has a built-in solver that powers its Hint button. We pointed it at #11982 and let it search without a limit. It examined every position that can be reached from the start, 61,643 of them, and none leads to a win. (We count two positions as the same when they differ only by which free cell or which empty column a card sits in, and cards go home automatically when it's safe, just as in the game.)

That agrees with every other exhaustive search: #11982 has no solution under the standard rules.

What would make it winnable

Two small changes turn #11982 into a winnable deal. Both are described in the FreeCell FAQ, and we confirmed both with Poozee's solver:

The second one is the surprising one. With just two cards swapped, the deal becomes winnable even with one free cell fewer than normal. It shows how much FreeCell depends on which Ace sits where, not just on how deep the Aces are.

How it was discovered

Microsoft FreeCell's help file says it is "believed (though not proven) that every game is winnable." In August 1994 Dave Ring started the Internet FreeCell Project to find out. He gave each volunteer a block of 100 consecutive deals and passed any unsolved ones on to his best players. More than 100 people took part, and when the project finished in April 1995, every deal had been solved except one: #11982.

The FAQ's author, Michael Keller, reports that it has since beaten probably thousands of human players and at least eight independent computer programs, most of them built to search exhaustively.

Other impossible deals

#11982 is the only impossible deal among the original 32,000, but later versions of FreeCell added more numbered deals. Among the first million there are eight impossible ones:

11982, 146692, 186216, 455889, 495505, 512118, 517776, 781948

That is roughly one in 125,000. There are also two joke deals: the Windows 95 version of FreeCell included deals numbered -1 and -2 that were deliberately unwinnable.

Try it yourself

You can play #11982 on Poozee: open FreeCell, click the Game # button, enter 11982 and press Deal. Press Hint and, after a few seconds of searching, the solver will tell you it found no winning line. New games on Poozee never deal #11982 by accident, because random games skip it.

Keep playing

Want a deal you can actually win? Every other classic FreeCell deal is solvable, and our FreeCell strategy guide shows how to plan one, starting with game #1. New to the game? Start with how to play FreeCell, or see how FreeCell's odds compare with Klondike in are all solitaire games winnable.