(10 pts)
In this problem, you’re going to modified the code in this Observable notebook to compute the number ways non-attacking kings can be placed on an m\times n board. To get your precise problem statement, choose your name from the following list:
I was asked to find the number of 9×6 chessboard and used this computation
board_cnt = math.multiply(
math.ones(21),
math.pow(math.matrix(kings_matrix(6)), 8),
math.ones(21)
)
to get board_cnt = 61643709
How many ways are there to place non-attacking Kings on a chessboard of dimensions 5 \times 9?
board_cnt = 4005785
board_cnt = math.multiply(
math.ones(89),
math.pow(math.matrix(kings_matrix(9)), 4),
math.ones(89)
)
The result is 4005785.
I was asked to find the number of 3 \times 4 boards. So I computed as follows:
board_cnt = math.multiply(
math.ones(8),
math.pow(math.matrix(kings_matrix(4)), 2),
math.ones(8)
)
That works out to be 93.
For a 7 x 6 chessboard,
board_cnt = math.multiply(
math.ones(21),
math.pow(math.matrix(kings_matrix(6)), 6),
math.ones(21)
)
board_cnt = 1382259
I was asked to find the number of 6 \times 9 boards. So I computed as follows:
board_cnt = math.multiply(
math.ones(89),
math.pow(math.matrix(kings_matrix(9)), 5),
math.ones(89)
)
Thant works out to be 61643709.
I was asked to find the number of 8 x 7 boards. So I computed as follows:
board_cnt = math.multiply(
math.ones(55),
math.pow(math.matrix(kings_matrix(8)), 6),
math.ones(55)
)
That works out to be 113555791
I was asked to find the number of ways to place non-attacking kings on an 8 X 5 board. I used the code below
board_cnt = math.multiply(
math.ones(13),
math.pow(math.matrix(kings_matrix(5)), 7),
math.ones(13)
)
The number of ways to do this is 795,611.
I was asked to find the number 7 \times 9 boards So I computed
board_cnt = math.multiply(
math.ones(89),
math.pow(math.matrix(kings_matrix(9)), 6),
math.ones(89)
)
Which works out to be 1,029,574,631 different boards
I was asked to find the number for 8 \times 9 boards. I did it as follows:
board_cnt = math.multiply(
math.ones(89),
math.pow(math.matrix(kings_matrix(9)), 7),
math.ones(89)
)
Which equals: 16484061769
I was asked to find the number of 5×6 boards. So I computed as follows:
board_cnt = math.multiply(
math.ones(21),
math.pow(math.matrix(kings_matrix(6)), 4),
math.ones(21)
)
That works out to be 31387
My board is 7x8.
The amount of different king placements on my board is 113,555,791.
board_cnt = math.multiply(
math.ones(55),
math.pow(math.matrix(kings_matrix(8)), 6),
math.ones(55)
)
There are 16484061769 ways to put non-attacking kings on a 8 \times 9 board.
This is generated with the following code:
board_cnt = math.multiply(
math.ones(fibonacci(8 + 2)),
math.pow(math.matrix(kings_matrix(8)), 8),
math.ones(fibonacci(8 + 2))
)
I had to find the number of 9 \times 5 boards. I computed
board_cnt = math.multiply(
math.ones(13),
math.pow(math.matrix(kings_matrix(5)), 8),
math.ones(13)
)
board_cnt = 4005785
I was asked to find the number of 9×7 chessboard and used this computation:
board_cnt = math.multiply(
math.ones(34),
math.pow(math.matrix(kings_matrix(7)), 8),
math.ones(34)
)
to get board_cnt = 1029574631
I was asked to find the number of 5 x 7 boards. So I computed as follows:
board_cnt = math.multiply(
math.ones(34),
math.pow(math.matrix(kings_matrix(7)), 4),
math.ones(34)
)
That works out to be 159651.
I was asked to find the number of 6 x 5 boards. So I computed as follows:
board_cnt = math.multiply(
math.ones(13),
math.pow(math.matrix(kings_matrix(5)), 5),
math.ones(13)
)
That works out to be 31387.
I was asked to find the number of 7 \times 7 boards. So I computed as follows:
board_cnt = math.multiply(
math.ones(34),
math.pow(math.matrix(kings_matrix(7)), 6),
math.ones(34)
)
That works out to be 12727570.
I was asked to solve the Kings Problem based on the dimensions 8 × 6. I used the following code to solve this:
board_cnt = math.multiply(
math.ones(21),
math.pow(math.matrix(kings_matrix(6)), 7),
math.ones(21)
)
The total number of different King placements is 9,167,119.