We can say that an n-by-n square is regular provided that:
Each of the integers from 0 to n2−1 appears in exactly one cell, and each cell contains only one integer (so that the square is filled), and
If we express the entries in base-n form, each base-n digit occurs exactly once in the units’ position, and exactly once in the n’s position.
What is an example of a 4-by-4 filled, magic square which is not regular? The square should use the integers 0 to 15. Show the answer in both decimal and base-4 as well.
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