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Jan2306   dakgootje: <johnthebon> for a similar story and others see also: http://www.seas.upenn.edu/~srihari/... 

Jan2306   dakgootje: <Marco65> He probably knew this, and only wanted one of us to say it ;) 

Jan2306   mr j: It took me a couple of mins and I was close to giving up. I found it hard to spot because I did not want to move the white queen away from the free capture of blacks knight. A good lesson for me to aim for the bigger fish! Nice Monday puzzel and I am enjoying these Math theorem postings :) 

Jan2306   LIFE Master AJ: Qg4! wins. (A good illustration of a double attack, Black cannot simultaneously defend the mate threat and protect his unguarded Queen.) 

Jan2306   likestofork: <dakgootje> Still waiting? Me, too, cause I've got a few complaints about the overall design, intelligent or otherwise. Yeah, the latter is definitely my suspicion. 

Jan2306
  Dim Weasel: Qg4 is so natural attacking continuation (did anybody find other candidate moves?) that I don't know if this is a puzzle at all (OK, come Wednesday my hybris will be cured ;) 

Jan2306   YouRang: Good old Mondays! Black resigns after being given the unhappy choice of losing his queen (for a bishop) or getting checkmated. 

Jan2306   jperr75108: I was just looking at problems like this with the CTArt 3.0 program. 

Jan2306
  kevin86: Maybe I am learning:In an earlier post,i seemed to have trouble with the puzzlenot so today! I immediately found the key movewith its direct threat of mate,and its veiled attack on black's queen. 

Jan2306
  keypusher: Quite apart from its merits as a puzzle, I am grateful to this problem for the funny and instructive kbitzes it generated! 

Jan2306   miguel12: TGIM! An easy puzzle to start my day and feel better about having to be at work. 

Jan2306   Dick Brain: I just love having a knight on f5 with white against black who has castled kingside; however, I am for some reason not as enthusiastic about a knight on c5 when black has castled queenside. 

Jan2306   TopaLove: <Dick Brain> Kasparov uses to say that it worths to give up a pawn to have a knight placed on f5. So it means it´s good! Really nice puzzle today! 

Jan2306   notyetagm: <TopaLove: <Dick Brain> Kasparov uses to say that it worths to give up a pawn to have a knight placed on f5. So it means it´s good!> If you want to see how powerful an f5knight can be for White with Black castled kingside, look no further than Sutovsky vs Smirin, 2002. 

Jan2306
  Gypsy: <George Danzig> revisited the mathematics he used to solve the two open problems in statistics again, after WW2, when he formulated the linear programming problem. It eventually led to the invention of the celebrated Simplex Algorithm! 

Jan2306   azaris: <celebrated Simplex Algorithm!> Yes. No method has been more used on so many problems to which it is mostly unsuitable since then. A true applied mathematician's hammer to every nail that comes along. 

Jan2306   Antipholous: Wow...this one took me forever. In fact...I didn't get it. Oh, well. It seems that Sundays are sometimes easy and Monday's are difficult at times. I'll be alright. I can see new tactical standpoints now. As I'm only rated 1301, I'm not that upset. 

Jan2306   Kaidra: For everyone of you that solves the puzzles in nanoseconds, there are hundreds that struggle with it or don't get it at all. True, some puzzles are simplistic, but getting a puzzle is far more enjoyable than not getting it. If all the puzzles were so hard that only GM's get them, then I (and I presume several others) would not be on this site. 

Jan2306   LivBlockade: I'm surprised that nobody's asked why Black didn't try to play on with 15...♗g5. If White plays 16. ♕xg5, then after 16...f6, material is even, or if 16. ♘h6+ ♗xh6; 17. ♕xd7 ♘xc1; followed by either 18. ♖axc1 ♗xc1; 19; ♖xc1 when Black has a Rook and Bishop for the Queen, or 18. ♕xc7 ♘e2+; 19. ♔h1 ♖ab8, and Black has 3 pieces against a Queen and Pawn assuming his Knight doesn't get trapped... 

Jan2306
  Richard Taylor: If anyone wants to solve things in nanoseconds try this link  http://chess.emrald.net/ 

Jan2306   yataturk: CB is being late today.... 

Jan2506
  keypusher: <azaris> <gypsy> I am hopeless in math but deeply impressed by mathematicians. Can you tell me more about the simplex algorithm? 

Jan2506   azaris: <keypusher> The algorithm itself is very simple and not very exciting, but the class of problems it solves (called linear programming or LP problems) can be used to formulate many different kinds of problems, hence it's rather useful. For example, assume that you have a zerosum game between two players. Then if both players have a variety of moves they can play in the game, we can construct a mixed strategy where both players choose their move randomly with different moves having different probabilities. Solving for an optimal mixed strategy then leads to a linear programming problem (von Neumann). 

Jan2506
  Gypsy: <keypusher> Consider a diamondlike object suspended in a multidimmesional space (maybe of tens of thousands of dimmensions). Many problems in mathematical economics, game theory, and applied math general reduce to the question of finding lowest points on such diamonds. This problem is known as the linear programming (LP) problem. In turn, Simplex algorithm is an efficient procedure of finding these lowest points, or determining there is none. Now the LP problem is actually the realy important notion here: <...People think that George [Dantzig] is a great man because he invented the Simplex algorithm, but he is an especially great man because he invented LP in the first place...> (Alan Hofman); Simplex is of secondary importance. One has to be a bit careful: The first mathematical article I know of that leads to a type of LP is a 1781 paper by G. Monge  a most remarkable and forth looking piece of work which anticipated about a half a dozzen of mathematical fields that were trully developed only later. Then LP was incidentally brushed on also by Fourier, Lagrange, Kantorovich, Koopmans, and Von NeumannMorgenstern. Koopmans and Kantorovich even received for their pioneering efforts on LP the Nobel prize in Economics. But George Dantzig is realy universally recognized as being the father of linear programming. The invention of Simplex algorightm actually came a couple of years after LP was formulated. There is a story of Dantzig visiting with John Von Neumann to ask for advice. After Dantzig's intial sentence or two to describe the problem Von Neumann just said: "Oh that!" and proceeded to give Dantzig lecture on many spects of linear programming, mostly connected with linear duality. Only at the end he explained to bevildered Dantzig that he has just finished a book with Morgenstern on Economics and Game Theory and that he immediately conjectured that something now called twoperson, zerosum games and linear programs will be found essentially equiavalent. (They nearly are completely equivalent, except for a small undecided glitch in the reduction from LPs into games.) The significance of Simplex method is that it realy solved the problem which was posed to it. It was not a completely trivial accomplishment, as be seen from the fact that Von Neumann did not have an algorithm avaiting already. In the two years of search for an efficient computational method, Von Neumann actually proposed to Dantzig an algorithm which, Dandzig later claimed, looked much like the recently celebrated algorithm by N. Karmarkar. (Dantzig was not able to prove their equivalence though.) Because of Simplex, many problems have been reduced to LP and, as <azaris> notes, a good number of those should not have been. That, of course, is hardly Dantzig's fault. 

Jan2506
  keypusher: <azaris>, <gypsy> Thanks! 



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