### Brain Teasers

# Mad Ade's Magic Square

Mad Ade placed the numbers 1-9 into a 3x3 grid, such that the four sides and the two diagonals each have the same sum (greater than 15.) What is the number in the center of the grid?

### Answer

3there is only one solution.

7 2 9

5 3 1

6 4 8

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## Comments

Really enjoyed it!

It's interesting that you can easily answer the teaser without actually constructing the magic square. I didn't have paper and pencil, but took less than 10 seconds to have the answer without them.

In order for the sums to exceed the average of 15, below-average numbers must go on the sides, which are only used for a single sum; above average must go in the corners, which are used for three sums; and probably something near the average in the center, which is used in two sums.

This arrangement means that both 8 and 9 will have to be in the same sum, so 1 must be the other number with 8 and 9 and the sum must be 18. From here it was obvious that the four corners to make the two diagonals must be 6,7,8,9. The two diagonals total 36 and 36 - (6+7+8+9) = 30. (36-30) / 2 = 3.

In order for the sums to exceed the average of 15, below-average numbers must go on the sides, which are only used for a single sum; above average must go in the corners, which are used for three sums; and probably something near the average in the center, which is used in two sums.

This arrangement means that both 8 and 9 will have to be in the same sum, so 1 must be the other number with 8 and 9 and the sum must be 18. From here it was obvious that the four corners to make the two diagonals must be 6,7,8,9. The two diagonals total 36 and 36 - (6+7+8+9) = 30. (36-30) / 2 = 3.

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