Author: Marc Bourzutschky
Date: 03:40:08 02/14/06
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On February 13, 2006 at 08:42:10, h.g.muller wrote: >On February 12, 2006 at 12:04:45, Marc Bourzutschky wrote: > >>We have also looked at "triplet leapers", combining three leapers into one. >>Here one can construct cases that win on an arbitrarily large board. However, >>it is only a finite set, and there are some triplets for which we are not sure >>whether they are a general win or not. I have run tablebases on up to 90x90 for >>some of these. >> >>-Marc > >OK, thanks for the info. I will look in to it, this is really fun stuff... :-) > >I suppose the cases where K + triple compound L can win on arbitrarily large >boards involve pieces that are able to all by themselves stop the bare King from >fleeing away, with enough time left to spare some moves for the other King to >make its approach. Such as a Squirrel ((0,2)+(1,2)+(2,2)), which can stop the >King for 2 moves by taking opposition. I guess this is an easy one to do even >without a computer, quite similar to the 'mechanical' way of mating with a Rook, >driving the King to a pre-chosen edge rank by rank. And about twice as tedious, >because where the Rook would fence off a rank once and for all, the Squirrel >would have to renew its position every 2 moves to achieve the same... Another winning case is (0,1)+(0,2)+(1,1), which is a little trickier to prove. However, there are cases, such as (1,3)+(2,3)+(3,3), (2,3)+(2,4)+(2,5), (0,4)+(1,4)+(2,4), (0,2)+(1,1)+(1,2), (1,3)+(2,2)+(2,3) that look to be winning but we have no proof. An example that is not winning is (2,2)+(2,3)+(2,4) which is a win on 55x55 but not 56x56. -Marc
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