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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