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Create a magic square of 4-digit numbers

Magic square with the position of 8 fixedMagic square with the position of 8 fixedMagic Matrices?The magic square with a holeUnsolved Mysteries: Magic Square of SquaresNo ordinary magic squaremodify a magic square - part IIA challenging Magic SquareCreate a 3x3 Magic Square that uses integers from -10 to -2Albrecht Durer Inspired Magic Square

.everyoneloves__top-leaderboard:empty,.everyoneloves__mid-leaderboard:empty,.everyoneloves__bot-mid-leaderboard:empty
margin-bottom:0;

.everyonelovesstackoverflowposition:absolute;height:1px;width:1px;opacity:0;top:0;left:0;pointer-events:none;

7

1

$begingroup$

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.

Similar puzzle link.

magic-square

share|improve this question

edited Sep 19 at 6:15

Sayed Mohd Ali

asked Sep 18 at 10:10

Sayed Mohd AliSayed Mohd Ali

1,22611 silver badge2020 bronze badges

$endgroup$

• 
  
  
  

  
  5
  

  
  
  
  
  
  

  
  $begingroup$
  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.
  $endgroup$
  – Rand al'Thor
  Sep 18 at 10:29
  

  
  
  
  

add a comment
 | 

7

1

$begingroup$

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.

Similar puzzle link.

magic-square

share|improve this question

edited Sep 19 at 6:15

Sayed Mohd Ali

asked Sep 18 at 10:10

Sayed Mohd AliSayed Mohd Ali

1,22611 silver badge2020 bronze badges

$endgroup$

• 
  
  
  

  
  5
  

  
  
  
  
  
  

  
  $begingroup$
  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.
  $endgroup$
  – Rand al'Thor
  Sep 18 at 10:29
  

  
  
  
  

add a comment
 | 

$begingroup$

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.

Similar puzzle link.

magic-square

share|improve this question

edited Sep 19 at 6:15

Sayed Mohd Ali

asked Sep 18 at 10:10

Sayed Mohd AliSayed Mohd Ali

1,22611 silver badge2020 bronze badges

$endgroup$

share|improve this question

edited Sep 19 at 6:15

Sayed Mohd Ali

asked Sep 18 at 10:10

Sayed Mohd AliSayed Mohd Ali

1,22611 silver badge2020 bronze badges

share|improve this question

edited Sep 19 at 6:15

Sayed Mohd Ali

asked Sep 18 at 10:10

Sayed Mohd AliSayed Mohd Ali

1,22611 silver badge2020 bronze badges

asked Sep 18 at 10:10

Sayed Mohd AliSayed Mohd Ali

1,22611 silver badge2020 bronze badges

asked Sep 18 at 10:10

Sayed Mohd AliSayed Mohd Ali

1,22611 silver badge2020 bronze badges

3 Answers
3

active

oldest

votes

11

$begingroup$

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!

share|improve this answer

edited Sep 18 at 20:09

answered Sep 18 at 16:13

hexominohexomino

69.6k66 gold badges194194 silver badges300300 bronze badges

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  That is the cleverest way to arrive at a solution that I've yet seen.
  $endgroup$
  – Brandon_J
  Sep 18 at 16:32
  

  
  
  
  


• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  $begingroup$
  Wow, the most elegant solution I've seen recently! :)
  $endgroup$
  – user47134
  Sep 18 at 17:16
  

  
  
  
  


• 
  
  
  

  
  3
  

  
  
  
  
  
  

  
  $begingroup$
  @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.
  $endgroup$
  – Brandon_J
  Sep 18 at 19:44
  

  
  
  
  

add a comment
 | 

1

$begingroup$

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.

share|improve this answer

answered Sep 19 at 8:08

Pʀıncess AnayaPʀıncess Anaya

45077 bronze badges

$endgroup$

add a comment
 | 

0

$begingroup$

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.

share|improve this answer

edited Sep 18 at 16:31

Brandon_J

8,19211 gold badge99 silver badges6060 bronze badges

answered Sep 18 at 13:08

ankitkanojiaankitkanojia

11722 bronze badges

$endgroup$

• 
  
  
  

  
  8
  

  
  
  
  
  
  

  
  $begingroup$
  Remember that the full square must contain nine of each digit 1, 2, 3, 4
  $endgroup$
  – Omega Krypton
  Sep 18 at 13:09
  

  
  
  
  


• 
  
  
  

  
  5
  

  
  
  
  
  
  

  
  $begingroup$
  ... and the diagonals don't make the same sum.
  $endgroup$
  – Weather Vane
  Sep 18 at 13:11
  

  
  
  
  

add a comment
 | 

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11

$begingroup$

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!

share|improve this answer

edited Sep 18 at 20:09

answered Sep 18 at 16:13

hexominohexomino

69.6k66 gold badges194194 silver badges300300 bronze badges

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  That is the cleverest way to arrive at a solution that I've yet seen.
  $endgroup$
  – Brandon_J
  Sep 18 at 16:32
  

  
  
  
  


• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  $begingroup$
  Wow, the most elegant solution I've seen recently! :)
  $endgroup$
  – user47134
  Sep 18 at 17:16
  

  
  
  
  


• 
  
  
  

  
  3
  

  
  
  
  
  
  

  
  $begingroup$
  @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.
  $endgroup$
  – Brandon_J
  Sep 18 at 19:44
  

  
  
  
  

add a comment
 | 

11

$begingroup$

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!

share|improve this answer

edited Sep 18 at 20:09

answered Sep 18 at 16:13

hexominohexomino

69.6k66 gold badges194194 silver badges300300 bronze badges

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  That is the cleverest way to arrive at a solution that I've yet seen.
  $endgroup$
  – Brandon_J
  Sep 18 at 16:32
  

  
  
  
  


• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  $begingroup$
  Wow, the most elegant solution I've seen recently! :)
  $endgroup$
  – user47134
  Sep 18 at 17:16
  

  
  
  
  


• 
  
  
  

  
  3
  

  
  
  
  
  
  

  
  $begingroup$
  @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.
  $endgroup$
  – Brandon_J
  Sep 18 at 19:44
  

  
  
  
  

add a comment
 | 

$begingroup$

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!

share|improve this answer

edited Sep 18 at 20:09

answered Sep 18 at 16:13

hexominohexomino

69.6k66 gold badges194194 silver badges300300 bronze badges

$endgroup$

share|improve this answer

edited Sep 18 at 20:09

answered Sep 18 at 16:13

hexominohexomino

69.6k66 gold badges194194 silver badges300300 bronze badges

answered Sep 18 at 16:13

hexominohexomino

69.6k66 gold badges194194 silver badges300300 bronze badges

answered Sep 18 at 16:13

hexominohexomino

69.6k66 gold badges194194 silver badges300300 bronze badges

1

$begingroup$

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.

share|improve this answer

answered Sep 19 at 8:08

Pʀıncess AnayaPʀıncess Anaya

45077 bronze badges

$endgroup$

add a comment
 | 

1

$begingroup$

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.

share|improve this answer

answered Sep 19 at 8:08

Pʀıncess AnayaPʀıncess Anaya

45077 bronze badges

$endgroup$

add a comment
 | 

$begingroup$

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.

share|improve this answer

answered Sep 19 at 8:08

Pʀıncess AnayaPʀıncess Anaya

45077 bronze badges

$endgroup$

share|improve this answer

answered Sep 19 at 8:08

Pʀıncess AnayaPʀıncess Anaya

45077 bronze badges

answered Sep 19 at 8:08

Pʀıncess AnayaPʀıncess Anaya

45077 bronze badges

answered Sep 19 at 8:08

Pʀıncess AnayaPʀıncess Anaya

45077 bronze badges

0

$begingroup$

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.

share|improve this answer

edited Sep 18 at 16:31

Brandon_J

8,19211 gold badge99 silver badges6060 bronze badges

answered Sep 18 at 13:08

ankitkanojiaankitkanojia

11722 bronze badges

$endgroup$

• 
  
  
  

  
  8
  

  
  
  
  
  
  

  
  $begingroup$
  Remember that the full square must contain nine of each digit 1, 2, 3, 4
  $endgroup$
  – Omega Krypton
  Sep 18 at 13:09
  

  
  
  
  


• 
  
  
  

  
  5
  

  
  
  
  
  
  

  
  $begingroup$
  ... and the diagonals don't make the same sum.
  $endgroup$
  – Weather Vane
  Sep 18 at 13:11
  

  
  
  
  

add a comment
 | 

0

$begingroup$

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.

share|improve this answer

edited Sep 18 at 16:31

Brandon_J

8,19211 gold badge99 silver badges6060 bronze badges

answered Sep 18 at 13:08

ankitkanojiaankitkanojia

11722 bronze badges

$endgroup$

• 
  
  
  

  
  8
  

  
  
  
  
  
  

  
  $begingroup$
  Remember that the full square must contain nine of each digit 1, 2, 3, 4
  $endgroup$
  – Omega Krypton
  Sep 18 at 13:09
  

  
  
  
  


• 
  
  
  

  
  5
  

  
  
  
  
  
  

  
  $begingroup$
  ... and the diagonals don't make the same sum.
  $endgroup$
  – Weather Vane
  Sep 18 at 13:11
  

  
  
  
  

add a comment
 | 

$begingroup$

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.

share|improve this answer

edited Sep 18 at 16:31

Brandon_J

8,19211 gold badge99 silver badges6060 bronze badges

answered Sep 18 at 13:08

ankitkanojiaankitkanojia

11722 bronze badges

$endgroup$

share|improve this answer

edited Sep 18 at 16:31

Brandon_J

8,19211 gold badge99 silver badges6060 bronze badges

answered Sep 18 at 13:08

ankitkanojiaankitkanojia

11722 bronze badges

edited Sep 18 at 16:31

Brandon_J

8,19211 gold badge99 silver badges6060 bronze badges

edited Sep 18 at 16:31

Brandon_J

8,19211 gold badge99 silver badges6060 bronze badges

answered Sep 18 at 13:08

ankitkanojiaankitkanojia

11722 bronze badges

answered Sep 18 at 13:08

ankitkanojiaankitkanojia

11722 bronze badges