From rusin@washington.math.niu.edu Mon Jan 9 11:51:40 CST 1995 Article: 15613 of sci.math Path: mp.cs.niu.edu!rusin From: rusin@washington.math.niu.edu (Dave Rusin) Newsgroups: sci.math Subject: Re: Minesweeper is driving me nuts. Date: 7 Jan 1995 17:47:43 GMT Organization: Northern Illinois University, Math Lines: 51 Message-ID: <3emk3v$ir7@mp.cs.niu.edu> References: <3edq9b$in3@news.doit.wisc.edu> <3elan2$8vg@mp.cs.niu.edu> NNTP-Posting-Host: washington.math.niu.edu In article <3elan2$8vg@mp.cs.niu.edu>, Dave Rusin wrote: ...nothing useful. (Mailreading from home makes me more prone to screw-ups). Here's what I intended to say: Whenever a new game enters the house, Daddy seems to disappear for a few days until he has analyzed it, run computer simulations, and so on. One time I taught the computer to play a solitaire game -- that is, I didn't play solitaire on the computer, I had the computer doing it. [It was a card game called 10-20-30 and I was interested in studying strategies.] Minesweeper was no exception last year. Claiming to be doing it 'for the kids' I wrote a simulation which would run on our old non-Windows machine. Along the way I tried to teach it how I solved the problem. An undocumented feature of the program allowed me to hit 'X' to automatically do the thinking I do methodically. Each time you make a move, you're solving a set of linear equations: one equation for each number revealed on the board, with one variable for each uncovered cell representing the number of bombs hidden there (0 or 1). What we do when playing is solve this system (partially) in a fast way. I wrote the computer program to carry out the tricks I knew. The program I posted will give you an indication of why I'm not a professional programmer. It's written in -- don't laugh now -- Turbo Pascal III. After I posted it (of course) I kept rummaging around and found a version produced a few days later, which has the eXpert option working correctly. It automatically handles situations like this: 1 1 ? ? ? ? and knows that the two cells in the last column are not bombs. Having already breached netiquette once by posting long code, I won't do it again, but if anyone wants I can send them the source or PC executable for this fancier version of my minesweeper solver. In examining the newer version I see it still fails to solve certain sets of equations; I think it's the ones which would require combining three or more at a time; for example, in 0 1 ? 1 2 ? ? ? ? you know the last cell is safe. I don't intend to pursue this project since the eXpert mode I have already works splendidly in many cases. Also, I have not addressed the question of how best to select the next square to uncover when you must make a guess. dave (always on the lookout for games amenable to mathematical analysis) (Anyone got Chutes and Ladders?)