Author: José de Jesús García Ruvalcaba
Date: 04:17:23 06/10/04
Go up one level in this thread
On June 09, 2004 at 17:18:55, Peter Berger wrote: >On June 09, 2004 at 13:24:54, José de Jesús García Ruvalcaba wrote: > >>On June 09, 2004 at 08:31:21, Peter Berger wrote: >> >>> >>>I enjoyed reading your posts but you generalized the problem too much IMHO. I >>>specifically referred to legal Swiss pairings only. I agree that there will >>>always be some way of pairing left but not one that also follows the much >>>stricter rules for Swiss pairings. >>> >>>If you have sufficient time you can look them up here: >>>http://www.fide.com/official/handbook.asp?level=C04 >>> >>>Peter >> >>Well, I did not generalise the problem too much. The FIDE swiss system rules are >>for sure strict, but they allow score brackets to be melted together if there is >>no other way of producing a pairing. Doing that succesvely until we get only one >>bracket (with n-3 rounds for n players that could easily happen according to the >>rules), we are in the situation I described. >> >>See >>http://www.fide.com/official/handbook.asp?level=C0401B >>B.3 is a relative pairing criterium. >> >>in C.13 of >>http://www.fide.com/official/handbook.asp?level=C0401C >>it is shown under which circumstances the last two score brackets are joined. >> >>And in 9.6 of >>http://www.fide.com/official/handbook.asp?level=C0402B >>it is described how and in which direction the median score group is extended. >> >>If you read carefully, in those pages the swiss system is described twice, and >>both descriptions are not equivalent. In one of them the score brackets are >>paired from up to bottom, in that case the C.13 rule is relevant. In the other >>one the brackets above the median group are paired from up to bottom, then the >>brackets below the median group are paired from bottom to up, and at the end the >>median group is paired, then is the 9.6 rule relevant. >>Anyway, as long as there is a pairing which does not break the absolute pairing >>criteria, there is a legal pairing. As I said, it can be guaranteed up to n-3 >>rounds. >>José. > >You sound pretty convincing José :) - I stand corrected I guess. > >Only thing that might possibly create additional problems for the mathematical >proof are the colour rules, especially the absolute ones. Three times the same >colour for a participant is never allowed without exceptions - a problem? > Yes, indeed. I stand corrected too, if you are too smart or have nothing useful to do I think you can create an example in which the absolute color rules prevent a pairing with n-3 rounds. For a first try I would suggest 8 players, 5 rounds and in the first two rounds white wins all games, or probably in rounds 3 and 4 white wins all games, or something like that. But that something like that actually happens looks extremely unlikely, if I were a phyisicist I would say that is despreciable. >Greetings to Goettingen, >Peter Greetings to Berlin, José.
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