Este post foi copiado do excelente Futility Closet. Na Geometria Projetiva, toda família de retas paralelas faz interseção em um ponto infinitamente distante. Compositores de problemas de xadrez na antiga Iugoslávia adaptaram esta ideia para o tabuleiro de xadrez, adicionando quatro casas especiais "no infinito".)
(This post has been copied from the excellent Futility Closet. In Projective Geometry, every family of parallel straight lines intersects at an infinitely distant point. Chess problem composers in the former Yugoslavia have adapted this idea for the chessboard, adding four special squares "at infinity".)
Uma Dama em um tabuleiro vazio, por exemplo, pode sair pelo Oeste (ou Leste) e atingir uma casa "no infinito", de onde ela ataca todas as linhas do tabuleiro simultaneamente, de ambas as direções. Ela também pode sair para o Norte (ou Sul) para atingir outra casa "no infinito", de onde ela ataca todas as colunas simultaneamente, novamente de ambas as direções. Finalmente, ela pode também sair pelo Noroeste ou Sudeste e atacar todas as diagonais paralelas a a8-h1, ou sair pelo Nordeste ou Sudoeste e atacar todas as diagonais paralelas a a1-h8. Estas quatro "casas do infinito", mais as 64 do tabuleiro regular, constituem o campo de jogo.
(A Queen on a bare board, for example, can zoom off to the West (or East) and reach a square "at infinity" from which she attacks every rank on the board simultaneously from both directions. She might also zoom to the North (or South) to reach a different square "at infinity"; from this one she attacks every file simultaneously, again from both directions. Finally she can zoom to the Northwest or Southeast and attack all the diagonals parallel to a8-h1, or zoom to the Northeast or Southwest and attack all the diagonals parallel to a1-h8. These four "infinity squares", plus the 64 in the regular board, make up the field of play.)
Seguindo as regras deste Xadrez Projetivo, Nenad Petrovic criou o problema abaixo, publicado em Matematika Na Shahmatnoi Doske. As Brancas jogam e dão xeque-mate em dois lances. Você consegue encontrar a solução?
(Following the rules of this Projective Chess, Nenad Petrovic created the problem below, published in Matematika Na Shahmatnoi Doske. White is to play and give checkmate in two moves. Can you find the solution?)
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| Nenad Petrovic, Matematika Na Shahmatnoi Doske (Xadrez Projetivo). Código FEN: 8/2n5/Pn1P1P2/2Q2P1P/2P2k2/3p4/P6K/8 w - - 0 1. |
PCFilho
Hint: with these extra four squares "at infinity", the Queen gains a lot of firepower.
ResponderExcluirWhite’s main task is to find a square where his own King is safely out of the way. But that’s quite tricky...
After 1. Kg1!!, Black has no safe move:
ResponderExcluirIf he moves the King to e4 or f3, then the Queen zooms westward to infinity and mates, attacking simultaneously from left and right on every rank.
If he moves the King onto the g-file then the Queen zooms southwestward to infinity, attacking simultaneously along all the southwest-northeast diagonals from both directions.
If he moves the d-Pawn then again the Queen can mate from the southwest/northeast.
If he moves the b6 Knight (anywhere), then the Queen zooms northwest and attacks along the northwest-southeast diagonals.
If he moves the c7 Knight then the Queen zooms north and attacks along the files.
Given all this firepower, White’s main task is really to find a square where his King is safely out of the way. But that’s tricky. After 1. Kh1?, for example, Black has 1. … Nbd5! and there’s no mate.