Put the nine numbers 0, 1, 2, 3, 4, 5, 6, 7 and 8 into the nine palace grid in the figure below. Add the three numbers in each row, column and diagonal to get eight sums. The sum of the eight sums is the largest______ .

Put the nine numbers 0, 1, 2, 3, 4, 5, 6, 7 and 8 into the nine palace grid in the figure below. Add the three numbers in each row, column and diagonal to get eight sums. The sum of the eight sums is the largest______ .


If the middle point of the nine palace grid is used for four times, fill in 8; if the four corners are used for three times, fill in 7, 6, 5, 4; if the four sides are used for two times, fill in 3, 2, 1, 0; if the maximum sum is 8 × 4 + (7 + 6 + 5 + 4) × 3 + (3 + 2 + 1 + 0) × 2 = 110



Fill in the nine figures 3, 7, 4, 1, 8, 9, 14, 4 and 15 in the nine palace grid, so that the number of each row, column and diagonal is equal to the number of each row, column and diagonal
And are equal


The sum of 9 numbers is 65, so the sum of each side, column and diagonal is 65 / 3, which is not an integer
The first condition for any n ^ 2 numbers to fill in the magic square of order n is that their sum can be divided by N. so I hope LZ can check the problem by himself



Fill - 1, 2, 3, 4, - 5, 6, 7, 8 and - 9 into the nine palace space respectively, so that the product of three numbers on each row, column and diagonal is negative


First line: - 1,2,3
The second line: 4, - 5,6
The third line: 7,8, - 9



Fill in the magic square and fill in the nine lattices of the magic square with the numbers - 4, - 3, - 2, - 1,0,1,2,3,4, so that the sum of all three numbers of horizontal, vertical, oblique and diagonal equals 0


-1 4 -3
-2 0 2
3 -4 1



Fill in the magic square below with - 8, - 6, - 4, - 2,0,2,4,6,8, which is the sum of all three numbers in horizontal, vertical, oblique and diagonal angles,
If we use - 2, - 1,0,1,2,3,4,5,6 to fill in the magic square, and the sum of all three numbers of all horizontal, vertical and diagonal angles is equal, how to fill in?


There are many answers to these questions
This is a third order magic square
such as
six hundred and eighteen
seven hundred and fifty-three
two hundred and ninety-four
Then - 8 corresponds to the first number, - 6 corresponds to the second 8 is the ninth
So it is
2,-8,6
4,0,-4
-6,8,-2
The back one is the same
-2 corresponds to 1, - 1 corresponds to 2 6 corresponds to 9
So it is
3,-2,5
4,2,0
-1,6,1



The magic square - 6 ~ 2 is negative 6 ~ 2. In a 3 by 3 lattice, there are 9 squares in total. It is required that the horizontal, vertical and oblique addition should be the same number


-5 2 -3
0 -2 -4
-1 -6 1



Fill - 8, - 6, - 4, - 2,0,2,4,6,8 into the magic square so that the sum of the three numbers of each row, column and diagonal angle is 0
Hurry. Do me a favor,


-2 8 -6
-4 0 4
6 -8 2



Put the nine numbers 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9 into the nine palace, add the three numbers in each row, column and diagonal to get eight sums. What is the maximum sum of the eight sums? (write the process)


The five numbers on the diagonal need to be added three times, and the other numbers only need to be added two times. The maximum sum is 4, 5, 6, 7 and 8 on the diagonal, so (0 + 1 + 2 + 3) * 2 + (4 + 5 + 6 + 7) * 3 + 8 * 4 = 110



Fill the nine numbers - 4. - 3. - 2. - 1.0.1.2.3.4 into the nine palace respectively, so that the three numbers of horizontal, vertical and diagonal angles add up to 0





Fill 0 + 1-1 + 2-2 + 3-3 + 4-4 in the Jiugong grid respectively, and the three numbers in each column are all 0


-1 4 -3
-2 .2
3 -4 1