Fill in nine grids from 1 to 9, so that the three numbers of the vertical and horizontal slopes are equal.

Method 1:

AlgorithmAnalysis:

Why is it the same as "15?

Set the sum of the first row to X; The sum of the second row to X; and the sum of the third row to X.

3x = 1 + 2 + 3 +... + 9 = 45 you added all the nine numbers.

We can see that the number at the center is 5 after X = 15.

Set S = to add the second row (center row) + add the second column (center column) + oblique add twice (X ).

You found that the number of centers is added four times, and the other is added once. (Three more centers are added)

S = 4x = 4*15 = 60 = 1 + 2 + 3 +... + 9 + number of centers * 3

Number of centers = 5

The Four Corners cannot be odd. Otherwise, a problem may occur when adding oblique values.

Because: if the upper left is an odd number, odd + 5 + right bottom number = 15 right bottom must be an odd number

In this case, if the upper right corner is an odd number, the lower left must be an odd number, and eventually all are an odd number,

If the upper right corner is an even number, the lower left must be an even number, and the remaining spaces are all even numbers.

There are 6 even numbers, but the even number is only 2, 4, 6, and 8.

Therefore, the four corners cannot be odd. Then, place the four corners into and.

Method 2:

Solve the above Indefinite Equation

Set

ABC

Def

Ghi

Then

A + B + C = 15

D + E + F = 15

G + H + I = 15

A + D + G = 15

B + E + F = 15

C + F + I = 15

A + E + I = 15

C + E + G = 15

The above indefinite equation can be calculated.

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