From: Steve Evans NETSPACE NET AU> Date: 22 feb 1999 Subject: Re: Solution to D29 (long) Colin Paul Adams wrote: > But my main reason for continuing this thread, is I though that people > might be interested in the process by which Steve and I edged towards > this solution. Well, I don't know of how much interest this is to some on the list. But here goes. > > >From my point of view, the problem started when Steve told me he had > been looking at it, but could not find the finishing mate. The first > 12 moves were the analysis Steve sent to me [snipped] along with > some of his comments: > > This is the (a?) sequence of moves that forces the King to the left hand > side of the board where common-sense dictates that there is a mate > involving the promotion of the Lance and Silver. > > 1. +RC-2j, +Gx2j; 2. S-2l, Kx2l (if K-1i 3. S-1k mate.); > 3. Kyx2j, K-3l; 4. R-3k, K-4l; 5. +RC-6j, +RCx6j (if K-5l > see below for mating sequence) 6. Ky-4j, K-5l; 7. R-5k, > K-6l; 8. Kyx6j, K-7l; 9. R-7k, K-8l; 10. Ky-8j, K-9l; > 11. Rx9k, K-10l; 12. Kyx10j, K-11l > [snipped] ...after this I get stuck. When I started I could instantly see that the solution involved far more depth than my program could reach. So I adopted an interventionist policy with the moves it was generating and used it pretty much just as a tool to explore and discard dead-end paths. The program quickly found the first few moves of the sequence for driving the King to the left of the board. After manually following this progression through (past the unexpected hurdle at move 5) to move 12 or 13, I was expecting the program to quickly find a mate. It didn't. So most of my efforts from here on were manual and I pretty much ignored the program's choice of moves. I've since discovered that had I just given the program its head and let it test each position to about 5 or 6 moves depth then followed its best moves it would have taken me right through to move 17 of the solution without any manual intervention at all. After that it was just a matter of bringing the +B down towards the King a step at a time until it was close enough to see the mate (the advancing of the +B was something the program couldn't deal with as there were too many moves involved). Shortly before contacting Colin I had looked at the possibility of bringing the +B down gradually towards the King, but each time I tried it I had over-ridden the computer's choice for move 16 (R-11i ) on the (incorrect) assumption that the Rook was going to need to be promoted before the final few moves. Had I left the computer's choice, I would have found the whole 38 (or is it 37?) move solution on the first attempt! As it was, I instead discarded the idea of the slowly advancing +B and decided that the problem (despite great promise) was insoluble. > Steve pointed out that on move 14 (did you see it, or was it the > computer?), the Rook can promote when it captures I spotted this one without my mechanical assistant! > Steve had previously said: > > I'm convinced that the sequence of moves through to 12 or 13 are correct but after that I > just can't work it out. My only thought is that there may be some way to bring the +B on 1a > into the action earlier on. This piece seems to be slightly out of position for the final > few moves. > As I said earlier, my attempts at bringing the +B down towards the King slowly (or quickly) always seemed to leave it slightly out of position for a mate. At this point I was wondering whether there was an early move somewhere that would leave it better placed. Basically, I was barking up the wrong tree here. > > I'll have another look at Ky - 10l, and see if I can't do something > with bringing the promoted Bishop in. > > Then after a few moments, I was ecstatic - this was it! So I composed > an email to Steve, confident I had got a wonderful solution. > > But as I wrote it out, I became aware that the mate depended upon > Black taking advantage of an interpretation of the repetition rule > that I made up on the spot (that the DEFENDER must vary). This was > disappointing. I decided to look closely at Colin's proposed solution and invest some more time examining the idea of repetition. In particular, I was hoping to find a move before 17 that would result in White transgressing and not Black. I decided that if, as Colin believed, the slow advance of the +B was important then there must be a better series of moves in the range 12 to 16. So, I started looking at them all manually, and then following the positions right through. Eventually, I tried the promotion and sacrifice of the Silver, followed soon after by the Kylin sacrifice to the Free Boar followed by Rook to 11i (as it turns out, the move sequence the program had been advocating all along) and then went on to find the solution manually (except for the last couple of moves where I brought the program back in for the coup de grace). > In addition, there was the fact that > the Rook didn't have to promote - This idea threw me as well. My underlying luddite tendencies (an odd trait in someone who writes computer programs, I know) led me to believe that there was clearly less chance of a mate with an unpromoted rook and so the computer failing to promote when it could do so was due to it's inherent short-sightedness. But, of course, it was right and I was wrong. > The role of humans co-operating is clearly shown here (I wouldn't have > started it if Steve hadn't done the first bit, and Steve would have > given up if I hadn't persisted). This is true. Without Colin sending me his ideas to test with the program, and his advocating the long haul approach with the +B (which I had already and falsely written off as a dead-end) the solution wouldn't have happened. > As for the machines, we must not forget that all the communications between Steve and myself > (which were vital - I would never have kept this up if we > had relied on snail-mail). Agreed. > And then there is Steve's computer program > (and the people who developed Zillions of Games), which had some role > in this I think (Steve - please enlighten us). Jeff Mallett and Mark Lefler, the designers of the Zillions-of-Games game playing engine have played a big part in this as well. Without the availability of their product I would have been unlikely to have attempted any of these glorious old mating problems. Steve Evans