A backtracking solver for the solitaire minigame in the incredible Shenzhen I/O.
Following Wikipedia's glossary of patience terms, I refer to any stack of cards as a pile. In the Shenzhen solitaire game, the cards start in 8 tableau piles of height 5. To win the game, the numbered cards must be collected in the 4 foundation piles. Finally, there are 3 cells where any card can be moved freely.
The notation r8 describes the red card rank 8. RR is a red dragon. f1 is the lone flower card.
Move cards [b3 g2] from pile 0 move to pile 3
RR -- GG f1 -- -- b1
g4 r9 BB g9 g6 g1 b5 GG
g8 r8 GG b2 r1 r3
r7 b7 b9 GG BB
r6 BB b8
g5 BB g7
r4 b6
b3 r5
g2 b4
g3
r2
I generated 1000 games and tried to solve them. Around 98% were soluble. On a 2015-spec computer, the median time to solve a game (or prove it insoluble) was 0.1 seconds. The 95th percentile was 6 seconds. A few games took much longer.
If it's of interest, I believe the game below is insoluble:
GG BB b4 g6 BB r7 RR b5
g1 RR r1 r6 g8 GG r5 GG
b2 g9 BB b3 g7 r3 BB r8
r4 g5 b8 b6 r2 b9 b1 g2
RR r9 f1 g4 g3 b7 GG RR