A 8-by-8 chessboard has two mirrors added on its left and right margin. The mirrors reflect the queen moves so that a queen threatens additional squares on the board. A queen threatens
- all squares in the same row or column
- all squares in the same diagonals
- all squares in the same diagonals reflected at one of the mirrors.
For example a queen in e2 threatens the e-column, the 2-row, the diagonal d1-to-h5, the reflection h5-to-e8 of this diagonal on the right mirror, the diagonal f1-to-a6 and the reflection a6-to-c8 of this diagonal on the left mirror.
What is the largest number of queens that can be placed on the 8-by-8 chessboard with mirrors so that no queen threatens another queen?