How is $a_{15}n_8e_9k_5f_{10}d_7b_4m_6$ a solution to the Eight Queens problem? J. W. L. Glaisher, On the Problem of the Eight Queens, Philosophical Magazine, 1847 says that each one of these terms (letter number combinations) that make up the solution, represent a square on a chessboard. But how do these terms represent a square on a chessboard? A chessboard only has 64 squares/cells, where a, b, c, d, e, f, g, and h are separate columns, consisting of 8 squares/cells each.
Let: a8 = top left corner, h8 = top right corner, a1 = bottom left corner, and h1 = bottom right corner.
So which squares do the terms that don't fit in this range represent?
*To clarify, I'm trying to figure out how to solve the eight queens problem using the determinant for a linear algebra research project, but I can't figure out how the terms given actually represent the solutions to the problem. Example: $a_{15}n_8e_9k_5f_{10}d_7b_4m_6$, what solution is this supposed to represent and how can I tell?
From the figure in the article, it appears that the NE-SW diagonals are numbered from $1$ to $15$, while the NW-SE diagonals are labeled with letters $a,b,c,d,e,f,g,h,k,m,n,p,q,r,s$
starting with the long diagonal and alternating below and above.
Converting from Glaisher's notation to standard chess notation:
$(a_{15},n_8,e_9,k_5,f_{10},d_7,b_4,m_6)=(h1,g7,f5,e8,d2,c4,b6,a3)$
which is a solution of the eight queens problem.
Glaisher's "a" is the a8-h1 diagonal, his "b" is a7-g1, "c" is b8-h2, "d" is a6-f1, "e" ia c8-h3, "f" is a5-e1, etc.; and his "1" ia a8-a8, "2" is a7-b8, "3" is a6-c8, "4" is a5-d8, "5" is a4-e8, "6" is a3-f8, "7" is a2-g8, "8" is a1-h8, "9" is b1-h7, "10" is c1-h6, etc. For example, Glaisher's $f_{10}$ is at the intersection of the a5-e1 and c1-h6 diagonals, i.e., the square d2.