Solutions of De Jaenisch′s problem on odd number grid (or chess board)

DOI：10.7511/dllgxb201802015

 作者 单位 李盘林,赵铭伟,徐喜荣,李丽双,李伯章

在德杰尼斯五后问题泛化研究基础上，给出了(2p+1)×(2p+1)奇数网格坐标表示，定义了解首格集，利用皇后控制或剩余控制数、马步格、解首格集，以及图形对称性，得到了奇数网格(或棋盘)德杰尼斯问题求解定理和求解方法，并给出了3×3网格、5×5网格和7×7网格德杰尼斯问题的1个、3个和24个基础解及其图示．结果表明奇数网格(或棋盘)德杰尼斯问题是网格优化管控问题之一，具有一定的理论价值和应用价值．

On the basis of the generalization research of De Jaenisch′s five queens problem, the coordinate representation of the (2p+1)×(2p+1) odd number grid is introduced, and the first grid set of the solution is defined. Using the control number and the remaining control number of the queen, lattice of the horse′s walking in Chinese chess, the first grid set of the solution, as well as the symmetrical properties of the figure, solutions and theorem of De Jaenisch′s problem on odd number grid (or chess board) are obtained. 1, 3 and 24 basic solutions of 3×3 grid, 5×5 grid and 7×7 grid of De Jaenisch′s problem shown in illustrations are given. The results show the De Jaenisch′s problem on odd number grid (or chess board) is one of the grid optimal control problems, and it has a theoretical value and prospects of good value.