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"Conversion" Magic Squares

Two years ago, MathNEXUS shared an unusal problem involving Magic Squares (actually posed to me by my graduate advisor...thanks Jack!).

The task was to extend the usual rules (i.e. the sums of the numbers in every row, every column, and every diagonal are equal) to create a 3 x 3 magic square where the products of the numbers in every row, every column, and every diagonal were equal.

Your New Task: Create a 3 x 3 Magic Square such that when each of the nine numbers in the cells is replaced by the number of letters in its verbal name (i.e. 9...nine...4), a new magic square is produced.

And: Can you use the same technique for similarily creating 4 x 4, 5 x 5, ...., n x n "Conversion" Magic Squares?

Note: Forgot to say that nine zeroes will not work, as the numbers in each of the nine cells have to be different.

 


Hint: I wish I knew enough about this problem to even provide a hint....If you come up with a good hint, please send it for inclusion...

 


Solution Commentary: I confess I have not solved this problem. All I know is that supposedly the "fifth-century druids" solved the problem!

Help!