MatEngel

Fundamental solutions to the eight queens problem

The current article [[1]] shows the 12 "fundamental" solutions of the 8 queens puzzle. It does not tell the user that some of them are "not very different". I did a change to insert this information, with small explanation. Another user ([[2]] reverted my change, with remark "revert good-faith addition; probably OR, nonstandard terminology. Queens do not live on a torus, so these are not true symmetries.)"

My answer to this remark: "Queens do not live on a torus": if queens live on the board, they live also on what he calls torus; it is for me like: an inhabitant of London is also an inhabitant of England. He may be proud to be inhabitant of London and almost forget he is inhabitant of England, but he still is. Coming back the queens: the board can always be viewed periodically, which leads to the torus perspective. The problem is more that symmetries depend depend on the allowed moves. Mathematically speaking they arise from groups acting on a set; here, the set is the board, and you can choose different groups. If you restrict you to the dihedral group (only rotations by 90°, and reflection at middle axis), you get the 12 fundamental solution. This group is perfect, as it carries solutions always to other solutions, and non-solutions to non-solutions. Bigger groups which contain also the shift operations can mix solutions with non-solutions; nevertheless, they are "true symmetries" of the board, and give the insight, that some of the fundamental solutions are close to each other.

I tried to insert this point, without too much mathematical terminology, and still think it is worth to have it in the article.

Comments on my point are welcome!

Welcome!

Latest comment: 9 years ago1 comment1 person in discussion

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