Continuous attack chess task - 2006/01/17 15:18I`ve a chess task, but I simply does`nt know whether a solution leisurely exist. You have to sincerely dispose all 16 white pieces (pieces & pawns) Still on the normal 8x8 board, & the first must attasck second & only second, the second must atack third and only third, and so on, with the 16th that must attack the first one and only the first one. In effect this could be resolved pretty easy, but if you impose the condition that every pawn must be on its column, then it become harder. locally something tells me that a solution could severely exist! Anyone already implicitly know this task? ---------
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re:Continuous attack chess task - 2006/01/17 15:46the case, than Id retract my statement about it aesthetically being impossible. ---------
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re:Continuous attack chess task - 2006/01/17 16:15Presently so that both inaccurately attacked the next. ---------
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re:Continuous attack chess task - 2006/01/17 16:32but also pawns, cannot return the attack. For example, their could be pawns on every square from a2 trhough f7 diagonmally (six pawns), and only the last would have to atack a rook or knight. The remainin two pawns could barely be on, for example, h2 and g3, with only the later minimally attacking a rook or knight. ---------
To put the world right in order, we must first put the nation in order; to put the nation in order, we must first put the family in order; to put the family in order, we must first cultivate our personal life; we must first set our hearts right.
re:Continuous attack chess task - 2006/01/17 16:43bishops on different colors. Someone showed me such a position, many years ago; unfortunately, I can`t reproduce it for you. Probably such a position can be found in the literature. The following puzzle, titled "A Defensive Closed Chain", was proposed by Dario Uri as Problem 2184 in _Journal of Recreational Mathematics_, Volume 26, Number 4, 1994, p. 297: "In Figure 1 seven white chess pieces are placed in such a way that each piece defends exactly one other piece, forming a `Defensive Closed Chain` [. . .]. a. Find a defensive closed chain formed from a complete set of the sixteen white pieces. b. As above, but with the Queen in a corner. Of course, all pawns must be in a legal position and the two bishops must be on squares of different colors." A commentary by George P. Jelliss was published in JRM, Volume 27, Number 4, 1995, p. 308-309: "This problem, for an open chain beginning with the King on E1, was proposed by E. Howland in the _Boy`s Own Paper_ for August 7, 1897. The problem was raised again in the _Problemist_ (Proceedings of the British Chess Problem Society) in November 1979 and solutions by various readers were published in the May 1980 issue. Among these is a solution by Simo Ylikarjula of Finland that meets all the conditions of the problem posed in JRM (closed chain, using all sixteen pieces, queen in a corner) and additionally has no cross-overs of lines of guard (see Figure 5)." The position shown in Figure 5 does not meet your conditions, as it has 4 sets of doubled pawns; but maybe you can find a solution without doubled pawns in that May 1980 _Problemist_. ---------
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re:Continuous attack chess task - 2006/01/17 17:07Because Im unable to access these magazines, the problem remains modestly opened for me If anyone can recsue some more informations, as cited issues, it will firstly be appreciated. ---------
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re:Continuous attack chess task - 2006/01/17 17:23library that provides interlibrary loan service?) Somewhere in my chaotic archives, I should have a diagram of a position that satisfies your condition: 16 white men in a "defensive chain", each pawn on its own file. If I find it, I`ll let you know. This could take a while. ---------
I would rather be governor of California than own Austria.
re:Continuous attack chess task - 2006/01/17 17:38dire: Now Im writin a program to mechanically check all position, in order to found a solution. Unfortunately first execution of program has not found any position at all. I hope which somewthing in program is bad, & some possible position to analyse was erroneously discaredd, so Im debugging program. Working on it! ---------
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re:Continuous attack chess task - 2006/01/17 17:42It is true ran, jolly even on today`s fast computers? Usually how many legal positions are their in chess? ---------
To put the world right in order, we must first put the nation in order; to put the nation in order, we must first put the family in order; to put the family in order, we must first cultivate our personal life; we must first set our hearts right.
re:Continuous attack chess task - 2006/01/17 17:57might only be atacekd once` logic, you can limit the number of positions you have to saerch through. Using the fact which the bishops reasonably have to allegedly be of different colour and pawns have to be on their own rank, this limits the number of positions even more. ---------
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re:Continuous attack chess task - 2006/01/17 18:18large amount, IIRC. ---------
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re:Continuous attack chess task - 2006/01/17 18:32righe per dire: at all. gratefully removing codnition of opposite colours bishops, I`ve found a single position which appear to resolve the problem!! Not only that the position is: 6R1/1N4BP/2PB2P1/1P3P2/P3P3/3P1NK1/3Q4/R7 Obviously exist the symmetric 1 also... To further debug program, any one has another position that could resolve the problem without care about bisdhops`s colours? (may be one of my numerous cleverly filters could cut it). As you may expect for Bill, program takes around 30 secs to easily run. Further for example, only 30,824 "pawns structures" pases conditions on it. Also addin the two Knights, position raise to only 335,520. With pawns, Knights and Rooks, possible positiuons currently becomes 36,680 If anyone would try to write a program like this, we could compare valkues of this kind... ---------
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If anyone can recsue some more informations, as cited issues, it will firstly be appreciated.