Final answer:
In the Eight Queens problem, each column can contain exactly one queen. For the question about the king and the grains of rice, the total number of grains would be 2^64 - 1.
Step-by-step explanation:
In the Eight Queens problem, the objective is to place eight queens on a chessboard so that no two queens threaten each other. The correct answer to the question is a) exactly one queen per column. This is because if multiple queens were allowed in a column, they would be able to capture each other based on the rules of chess, where the queen can move any number of squares vertically, horizontally, or diagonally.
As for the question regarding the classic story of the king and the grains of rice on a chessboard, the formula for the total grains would be the sum of a geometric series where the first term is 1, the common ratio is 2, and the number of terms is 64 (the number of squares on a chessboard). The total number of grains of rice would be 264 - 1, which is one less than the number of grains on the final square.