# Create a magic square of 4-digit numbers

Example:

4567 4567 4567
4567 4567 4567
4567 4567 4567

what is magic square? if you add up each diagonal, row and column of above matrix it will sum upto 13701.

Above is a 3*3 matrix where each entry is the same number. You need to replace the "4567"s with 9 different 4-digit numbers to create a perfect magic square.

Remember that the full square must contain nine of each digit 1, 2, 3, 4, and that all nine entries must be four-digit integers.

You need to use only the four digits 1, 2, 3, 4 to solve the problem so that we won't end up with multiple solutions.

You can use numbers like 1234, 4321, 2211, 2121 and so on. But if you used 4321 once in any of the 9 cells you cannot use it again.

• I've just made an edit, attempting to make your question more clear/coherent/comprehensible. Please let me know if the question as it's now written is what you intended. – Rand al'Thor Sep 18 '19 at 10:29

Building on the strategy of Omega Krypton, this is one possibility which also gets the diagonals to sum to the magic total

1214 3134 2324
3334 2224 1114
2124 1314 3234

To clarify, the sum of the numbers in each row, each column and along each diagonal is 6672 (the magic total) and each of the digits 1,2,3,4 appears nine times.

First of all, construct four single digit magic squares...

132
321
213

213
321
132

132
321
213

444
444
444

Then concatenate them to get a 4-digit magic square!

• That is the cleverest way to arrive at a solution that I've yet seen. – Brandon_J Sep 18 '19 at 16:32
• Wow, the most elegant solution I've seen recently! :) – user47134 Sep 18 '19 at 17:16
• @SayedMohdAli I rather think an explanation of what a magic square is would be up to you as the puzzle-poser. Granted, I don't think it would hurt for hexomino to include the final magic square in his answer. – Brandon_J Sep 18 '19 at 19:44

Here is another one

2243 1341 3142
3141 2242 1343
1342 3143 2241

All rows, columns and diagonal sums 6,726 and there is only 9 of each 1, 2, 3, 4

I will edit the explaination later.

I think this is the answer where each number consisting of 4 digits with only 1,2,3,4 number and calculation of this 3*3 matrix will be equals from each side maybe this the combination of digits which can be considered as a magic number.

• Remember that the full square must contain nine of each digit 1, 2, 3, 4 – Omega Krypton Sep 18 '19 at 13:09
• ... and the diagonals don't make the same sum. – Weather Vane Sep 18 '19 at 13:11