# queens Test Program

In the modern chess play the queen piece has the most power, as
it can move along the diagonals, the verticals and the
horizontals. It thus combines the power of the bishop piece and
the rook piece. Instead of playing chess the chess board can also
be used to pose riddles. One such riddle asks for the placement of
nine queens so that they don’t attack each other. Here is a
solution on the 4x4 checker board:

Picture
15: 4 Queens

The solution algorithm works similar to the solution algorithm
for the Sieve of Eratosthenes in that occupied places are crossed
out. The difference is that backtracking is involved in the
placement of the queens and that we do not represent the whole
board. Only the distinct positions of the placed queens are
remembered in a list, which makes the check for horizontal and
vertical obsolete. The diagonal check is then implemented via
arithmetic.

One test iteration will compute all 352 solutions for the 9x9
checker board.

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