Fill in the blanks with the number 123456789 so that the following equation holds The number of each space should be different

Fill in the blanks with the number 123456789 so that the following equation holds The number of each space should be different


According to the ratio of the three numbers, we can determine the number of hundreds: 246, that is, 2 □ □ = 1 / 2 * 4 □ □ = 1 / 3 * 6 □, the remaining: 1,3,5,7,8,9, the ten digit number: can only be 135, that is, 21 □ = 1 / 2 * 43 □ = 1 / 3 * 65, the remaining 789, of which 8 must be assigned to the second number [according to the coefficient 1 / 2] to get three complete numbers



Can I fill in the number 1, or 2, or 3 in each space on the 8 × 8 chessboard, so that the sum of each number on each row, column and two diagonal lines is different? Please give reasons


Note that there are 18 "lines" in 8 rows, 8 columns and two diagonals. Each line has 8 numbers. In order to make the sum of numbers on each line different, there are more than 18 kinds of possibilities. But we only fill in 1, 2 and 3 kinds of numbers. Therefore, among the 8 numbers on each line, the minimum sum is 8



Fill 9 consecutive natural numbers starting from 1 into the 9 spaces in the figure below, so that the sum of three numbers in each row, column and two diagonals is equal
I want not only the answer, but also the process


You can add nine numbers and divide them by the number of rows. The number you get is the sum of the numbers in each row (called magic number)
That is to say, (1 + 2 + 3 +.. + 9) / 3 = 15
The diagonal sum of each row and column is 15
4 9 2
3 5 7
8 1 6
We have all the answers and methods