Hello everyone,
I've been working on various FreeCell projects for more than a year. A few months ago, I started my attempt to solve by computer all FreeCell Pro deals with four freecells, and to find all of the impossible deals. I have finally completed the computation, and I found 102,032 impossible deals, as well as 46 intractable deals. Here is the list:
https://drive.google.com/folderview?id=0B6WZWNModsLfaEIzbnM5UkpHek0&usp=drive_web
I used Tom Holroyd's solver in FreeCell Pro. The newer versions of Shlomi Fish's solver are much faster and I would have liked to use it, but I found that its deal numbers only match FreeCell Pro's from deals 0 to 2147483647, and then it cycles between those deals, so its deal number 2147483648 is the same deal as deal number 0. I was able to speed up the computation process by solving different ranges of deals on multiple copies of the program, and I also had two computers to do the work on.
I found 48 deals which could not be resolved by Holroyd's solver using 2 GB of memory. The first two such deals, 53687601 and 186461199, are known to be impossible. One particularly curious deal is 2303926468, which I could not definitively resolve with either three or four freecells.
I was surprised to find some impossible deals not on Shlomi Fish's list of impossible deals, while I found no new winnable deals. I also found some winnable deals which are considered impossible by the Woods-Ettlinger solver in FreeCell Pro, such as 93877578 and 1129622823.
Finally, it definitely deserves to be mentioned that there are six FreeCell Pro deals impossible with five freecells. They are 14720822, 647519280, 3015622123, 5705339228, 7273316239, and 7573544118. All of them can be won with six freecells. It should be noted that 3015622123 is impossible with four freecells and one empty column, while 7273316239 can be lost with six freecells by playing a bad first move. Those two deals are probably the most difficult of all FreeCell Pro deals.
Received on Mon Jul 11 2016 - 12:31:32 IDT