Unsolvable Free Cell Games

There seems to be some uncertainty over whether all Free Cell games are solvable. The answer is no. Here are some unsolvable ones.

Example 1

With all the cards in play.

A♠	A♥	A♣	A♦	Q♠	Q♥	Q♣	Q♦
3♠	3♥	3♣	3♦	10♠	10♥	10♣	10♦
5♠	5♥	5♣	5♦	8♠	8♥	8♣	8♦
7♠	7♥	7♣	7♦	6♠	6♥	6♣	6♦
9♠	9♥	9♣	9♦	4♠	4♥	4♣	4♦
J♠	J♥	J♣	J♦	2♠	2♥	2♣	2♦
K♠	K♥	K♣	K♦

Suits are irrelevant. All cards of the same rank of any suit ( ♠, ♥, ♣, or ♦) can be swapped.

No adjacent number pairs can be reached.

Example 2

With the aces removed.

K♠	K♥	K♣	K♦	2♠	2♥	2♣	2♦
J♥	J♣	J♦	J♠	4♥	4♣	4♦	4♠
9♣	9♦	9♠	9♥	6♣	6♦	6♠	6♥
7♦	7♠	7♥	7♣	8♦	8♠	8♥	8♣
5♠	5♥	5♣	5♦	10♠	10♥	10♣	10♦
3♥	3♣	3♦	3♠	Q♥	Q♣	Q♦	Q♠

Colours are important but suits are not. So

Black cards ( ♠ or ♣) can be swapped for black cards
Red cards ( ♥ or ♦) can be swapped for red cards
Black cards cannot be swapped for red cards

A maximum of 9 non-trivial moves are possible:

3♠ → Hand
5♦ → Hand
7♣ → Hand
Q♥ → Hand
9♥ → 10♠
J♠ → Q♦
Q♣ → K♦
10♥ → J♠
8♠ → 9♥

An inferior variant yeilds 7 non-trivial moves:

3♠ → Hand
5♦ → Hand
7♣ → Hand
9♥ → Hand
J♠ → Q♦
Q♣ → K♦
10♥ → J♠

If a queen is picked up first, one move will be possible.

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