If every column, row every diagonal adds up to same number n and the middle number is 8 of a 3x3 grid then what is n?

Question

Nine consecutive integers are placed in the nine squares of a 3x3 grid. If every column, every row, and every diagonal adds up to the same number n and the middle number is 8 what is n?

Answer 1

Numbers 4 to 12 and n=24

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Answer 2

Since 8 is common for half of the lines we can conclude that by symmetry the list of consecutive numbers should begin with 4 with 8 in the middle.
4, 5, 6, 7, 8, 9, 10, 11, 12
This means for lines that has 8 in it we need extreme values to pair in each line like [4(lowest) , 12(highest)],
[5(2nd lowest) , 11(2nd highest)] to obtain a number that can be reproducible ie.,
8 + 4 + 12 = 24
8 + 5 + 11 = 24
8 + 6 + 10 = 24
8 + 7 + 9 = 24.
Therefore n = 24
Now to do the table we need a diagonal where the value is changing the least 9, 8, 7 will do
Now we have to balance the 3 cells on each side of the diagonal with values that maintain balance.

Comments

not all equal to 15!

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What do you mean?

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Oh got it! Thanks.

Answer 3

Another solution:
Since 8 in the middle, the rest 8 numbers will be from 8-4=4 to 8+4=12
We put them into 3x3 grid in increasing order then the picture below will show self explanatory steps to get all numbers into right grids. Finally we get n=24 in any direction

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