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A predecessor: the 8 queens problem

A famous problem in chess is to arrange 8 Queens in 8*8 chess board, which is known to be 8 queens problem. Here, in this 8 Queens problem an individual should arrange 8 Queens in chess board without the interaction of other Queens. Each Queen should not meet other queens. The following board shows the output for 8 Queens problem,

This Eight Queens problem is famous all along and also it has its own history. This problem has been included in education.

To celebrate these nine years of chess variant webpages, they conducted a small contest: to look for the best solution to The 9 Queens Problem.

One queen more

The 9 queens problem, placing 9 queens without interaction in 8*8 chess board is impossible, so the team allowed to use pawns to add on the board to solve the puzzle. Now the solutions were too many. Finally the team announced to use less pawns to solve the puzzle and win the contest.

Roberto Lavieri has proved 10 Queens with 2 pawns. His solution follows, Place the QUEENS: a8, b5, c3, d1, d6, e4, f2, f7, g5, h3 PAWNS: d5, f3. He said a big no to find the solution for 9 Queens problem in 8*8 chess board with one pawn. With two Pawns he constructed this solution: QUEENS in a1, b3, c5, d3, d8, e6, f4, g2, h5. PAWNS in c3, b5 and also he mentioned as he don't have a proof for this solution.

More possibilities are there in n Queens problems with n*n chessboard.

Number of Total Solutions to the Queen's Problem:

Board | Total Solutions | Unique Solutions |

1 x 1 | 1 | 1 |

2 x 2 | 0 | 0 |

3 x 3 | 0 | 0 |

4 x 4 | 2 | 1 |

5 x 5 | 10 | 2 |

6 x 6 | 4 | 1 |

7 x 7 | 40 | 6 |

8 x 8 | 92 | 12 |

9 x 9 | 352 | 46 |

10 x 10 | 724 | 92 |

11 x 11 | 2,680 | 341 |

12 x 12 | 14,200 | 1,787 |

13 x 13 | 73,712 | 9,233 |

14 x 14 | 365,596 | 45,752 |

15 x 15 | 2,279,184 | 285,053 |

16 x 16 | 14,772,512 | 1,846,955 |

17 x 17 | 95,815,104 | 11,977,939 |

18 x 18 | 666,090,624 | 83,263,591 |

19 x 19 | 4,968,057,848 | 621,012,754 |

20 x 20 | 39,029,188,884 | 4,878,666,808 |

21 x 21 | 314,666,222,712 | 39,333,324,973 |

22 x 22 | 2,691,008,701,644 | 336,376,244,042 |

23 x 23 | 24,233,937,684,440 | 3,029,242,658,210 |

24 x 24 | 227,514,171,973,736 | 28,439,272,956,934 |

25 x 25 | 2,207,893,435,808,350 | 275,986,683,743,434 |

26 x 26 | 22,317,699,616,364,000 | 2,789,712,466,510,280 |

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Daily Maths Topic Today - contest: the 9 queens problem.