Adding up to 15

How can you place the numbers 1 through 9 in a 3×3 grid such that every row, column, and the two diagonals all add up to 15?



To solve this riddle, it first seems logical to put number 5 in the middle square becuase it is the median and mean of the numbers from 1 to 9 (and also the average of any 3 numbers adding up to 15).

The next thing to do is place the 1 since it’s the smallest and will thus be likely to quickly constrain what we can do afterward. We can try to place the 1 in either a side square or a corner square, but once we place it, it forces us to place the 9 on the opposite side. At this point, we just play around with the remaining numbers to see if we can work out a solution (there aren’t many possibilities remaining for where we can place the other numbers).

Going along these lines, we’ll quickly get to a solution. This image shows how to place the numbers.


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