Is there a Sudoku Principle?
in [Math]
|
Prev: FINALLY A NEW "PRIMALITY FORMULA" AND PRIME NUMBER DISTRIBUTION FORMULA-- FROM HOPE RESEARCH TO BE RELEASED THROUGH PROFESSOR EDGAR ESCULTUR PHD, MADISON, WISCONSIN
Next: Sruttura T,U.N.Ze.
From: David R Tribble on 21 Jun 2010 19:08 Ludovicus wrote: >> As there is a Pigeon-hole Principle, I think a new util principle can >> be based in the practice of Sudoku: >> "If n cells must be filled with n elements and n-1 cells are >> prohibited to one of those, then that element must fill the free cell." > Arturo Magidin wrote: >> "Once the impossible has been eliminated, whatever remains, however >> unlikely, must be the truth" seems to have anticipated you by 100+ >> years... > Herman Jurjus wrote: > More like 2200+ years (Chrysippus' dog). An interesting quote for Chrysippus (from Wikipedia): | He determined one of the principle features of the infinite | set: since a man and a finger have an infinite number of | parts as do the universe and a man, it cannot be said that | a man has more parts that does his finger, nor that the | universe has more parts than a man. http://en.wikipedia.org/wiki/Chrysippus
From: Herman Jurjus on 22 Jun 2010 06:16 On 6/22/2010 1:08 AM, David R Tribble wrote: > Ludovicus wrote: >>> As there is a Pigeon-hole Principle, I think a new util principle can >>> be based in the practice of Sudoku: >>> "If n cells must be filled with n elements and n-1 cells are >>> prohibited to one of those, then that element must fill the free cell." >> > > Arturo Magidin wrote: >>> "Once the impossible has been eliminated, whatever remains, however >>> unlikely, must be the truth" seems to have anticipated you by 100+ >>> years... >> > > Herman Jurjus wrote: >> More like 2200+ years (Chrysippus' dog). > > An interesting quote for Chrysippus (from Wikipedia): > | He determined one of the principle features of the infinite > | set: since a man and a finger have an infinite number of > | parts as do the universe and a man, it cannot be said that > | a man has more parts that does his finger, nor that the > | universe has more parts than a man. > > http://en.wikipedia.org/wiki/Chrysippus People who are interested in this kind of anticipations of 'modern' ideas in antiquity should absolutely know about this one as well: Lucio Russo, La Rivoluzione Dimenticata (The Forgotten Revolution), 1996 (Review here: http://www.ams.org/notices/199805/review-graffi.pdf ) -- Cheers, Herman Jurjus
From: The Qurqirish Dragon on 22 Jun 2010 08:24
On Jun 21, 10:04 am, Ludovicus <luir...(a)yahoo.com> wrote: > As there is a Pigeon-hole Principle, I think a new util principle can > be based > in the practice of Sudoku: > "If n cells must be filled with n elements and n-1 cells are > prohibited to > one of those, then that element must fill the free cell." > Ludovicus This sounds like a formalization of the the "pinned squares" technique. I have seen this term used in many places, but it is described and illustrated at brainbashers.com in the sudoku help. The locked set technique says that if there is only one position in a row/column/block that is permitted to have a particular value, then that cell must have that value. There is also a dual to this strategy called "forced moves", which says if only one value is allowed in a space, then it must go there. Third, there is an extension of this called "locked sets" which says that if there are a group of m cells within a row/column/block that together can only have m different digits, then those digits cannot appear anywhere else in that row/column/block. Your original idead is this situation with the case m = n - 1. |