TOT 103 1985 Autumn J7 S7 super-chess, 30 x 30 board, 20 different pieces
Source:
August 26, 2019
game strategygamecombinatorics
Problem Statement
(a)The game of "super- chess" is played on a board and involves different pieces. Each piece moves according to its own rules , but cannot move from any square to more than other squares . A piece "captures" another piece which is on a square to which it has moved. A permitted move (e.g. squares forward and squares to the right) does not depend on the piece 's starting square . Prove that
(i) A piece cannot cap ture a piece on a given square from more than starting squares.
(ii) It is possible to arrange all pieces on the board in such a way that not one of them can capture any of the others in one move. (b) The game of "super-chess" is played on a board and involves different pieces. Each piece moves according to its own rules , but cannot move from any square to more than other squares. A piece "captures" another piece which is on a square to which it has moved. It is possible that a permitted move (e.g. squares forward and squares to the right) may vary, depending on the piece's position .
Prove that one can arrange all pieces on the board in such a way that not one of them can capture any of the others in one move.( A . K . Tolpygo, Kiev)PS. (a) for Juniors , (b) for Seniors