Explanation Given: It is given that n is a positive integer that can’t exceed 10 . n -queens problem is to arrange n -queens on an n × n chessboard so that no two queens can attack each other by being in same row, same column or diagonal. For n = 1 problems has trivial solution, because it has only one queen, for n = 2 and n = 3 has no solution because it is not possible to arrange two or three queens in such manner that they don’t attack each other by being in same row, column or diagonal. For n=4, the total chessboard boxes are 4 × 4 = 16 , 4 queens can be place on 16 with no restriction = 16 C 4 = 1820 If we can place one queen in one row, then the number of combinations will be 4 4 = 128 If we can place one queen in one row and one queen in one column then the number of combinations will be 4 ! = 4 × 3 × 2 × 1 = 24 Now if we add one more restriction that no queen can be in same diagonal then we can check for right to left diagonals as | i − j | should be unique and left to right diagonals as | i + j | should be unique

Discrete Mathematics and Its Applications ( 8th International Edition ) ISBN:9781260091991

8th Edition

ISBN: 9781259676512

Author: Kenneth H Rosen

Publisher: McGraw-Hill Education

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Chapter 11, Problem 6CAE

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The number of different ways n queens can be arranged on an n×n chessboard so that no two queens can attack each other for all positive integers n not exceeding 10.

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Discrete Mathematics and Its Applications ( 8th International Edition ) ISBN:9781260091991

Ch. 11.1 - Prob. 1E Ch. 11.1 - Vhich of these graphs are trees?Ch. 11.1 - Prob. 3E Ch. 11.1 - Prob. 4E Ch. 11.1 - Prob. 5E Ch. 11.1 - Prob. 6E Ch. 11.1 - Prob. 7E Ch. 11.1 - Prob. 8E Ch. 11.1 - Prob. 9E Ch. 11.1 - Prob. 10E

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The number of different ways n queens can be arranged on an n × n chessboard so that no two queens can attack each other for all positive integers n not exceeding 10 .

Solution Summary: The author explains how n -queens can be arranged on a chessboard so that no two queens attack each other by being in same row, column or diagonal.

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The number of different ways n queens can be arranged on an n×n chessboard so that no two queens can attack each other for all positive integers n not exceeding 10.

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