[This game is Part 3 of 3 of The Sorcerer's Puzzles III. See "Bricks"
and "Gordian Knot" for Parts 1 and 2.]
(From Color Computer Magazine, September 1983.)
by Richard Ramella
"It's getting late," said Sorcerer Goldberg. "And now for the tale
of..."
64 WITCHES
The annual witches' convention on Bald Mountain was thrown into
disarray when 64 witches showed up for a meeting in a hall containing
64 chairs in an eight-by-eight grid.
"I don't understand all the fuss," said Gaspar the (friendly) host.
Eight witches stood before him. Each was dressed in a different
color: yellow, blue, red, buff, cyan, magenta, orange, and black.
Each represented seven of his sisters dressed similarly.
"The problem," said the yellow witch, "can be understood if you
pretend we witches are all queens -- chess pieces -- and the
eight-by-eight rows of chain are squares on a chessboard."
"Yes?" said Gaspar, who was above average in intelligence.
"Then you must seat us so that no two are in a line where one could
take the other by making a legal queen's move."
"I see," said Gaspar, "no two in the same diagonal line or orthogonal
line -- up and down and sideways."
"Right-o," said the blue witch. "That rule only applies to each set
of same-colored eight witches. For example, red and blue witches may
sit in the same rows. After the yellow witches are seated correctly,
then another set must be seated, and so on."
"I'll try," Gaspar said.
"What more can we ask?" shrugged a red witch.
Gaspar approached the problem by pretending the hall was an orange
square in a computer display. To start, a yellow square appeared in
the northwest corner. He maneuvered it with the four arrow keys, and
set it in position by tapping S. He erased the square from a set
position by tapping E. When he made a mistake, the witch refused to
stay seated. As easy set of eight witches was successfully seated,
the cursor turned to the next color. At any time he could end by
tapping T, and replace the room with a scoreboard showing the Point
values of the colors already set, in case Gaspar wanted to save the
position and try again at another time.
"I think perfection is impossible here," Gaspar said, "but a
signficantly high score certainly isn't." He set to work.
"And now for the tests," said Sorcerer Goldberg to Poke and Sunflower
as he closed the book. Then he noticed both children had falled
asleep before the fire. "Oh well, there's no hurry; these tests will
take a awhile, anyway."