There are magic, antimagic, multimagic or satanic, and even alphamagic squares. There are also squares within squares, squares made by prime numbers and square made up by pandigital numbers like that achieved by Rodolfo Kurchan
The latter is unique, being made by Pandigital numbers, if you count the number of occurrences of each digit, we see that obviously is the same for all, that is, around the square there are exactly sixteen zeros, sixteen ones, etc. .
Based on this square I started to look for magic squares of order three in which all digits appear the same number of times.
So I found these magic squares:
a) Magic square in that each digit appears twice
109 32 87
54 76 98
65 120 43
b) Magic squares in which each digit appears exactly three times
Also in this squares each column and row each digit appears only once
1645 203 987
287 945 1603
903 1687 245
1542 306 978
378 942 1506
906 1578 342
1560 342 978
378 960 1542
942 1578 360
1560 348 972
372 960 1548
948 1572 360
1572 360 984
384 972 1560
960 1584 372
The last magic square that I've found is the only one such in each column and row are digits that appears twice, but is the only one that in one diagonal each digit appears only once.
1329 276 996
534 867 1200
738 1458 405
c) Magic squares in which each digit appears exactly four times
22950 204 18156
8976 13770 18564
9384 27336 4590
14399 2244 10285
4862 8976 13090
7667 15708 3553
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