Ultra bimagic 25x25 square

 

Harm Derksen introduced on his website http://www.math.lsa.umich.edu/~hderksen/magic.html an ultra bimagic 25x25 square. The 25x25 magic square is panmagic and each 1/5 row/column/diagonal gives 1/5 of the magic sum. Fill in digit x digit instead of each digit and each row/column/diagonal gives the bimagic sum of 3263025.

Use 2x the same or 2 different panmagic 5x5 squares to construct the ultra bimagic 25x25 square. Each grid consists of 25x the (on the 2x2 carpet) shifted versions of the panmagic 5x5 square.


2x2 carpet of first panmagic 5x5 sq.    2x2 carpet of second panmagic 5x5 sq.

25

1

7

13

19

25

1

7

13

19

   

1

15

22

18

9

1

15

22

18

9

12

18

24

5

6

12

18

24

5

6

   

23

19

6

5

12

23

19

6

5

12

4

10

11

17

23

4

10

11

17

23

   

10

2

13

24

16

10

2

13

24

16

16

22

3

9

15

16

22

3

9

15

   

14

21

20

7

3

14

21

20

7

3

8

14

20

21

2

8

14

20

21

2

   

17

8

4

11

25

17

8

4

11

25

25

1

7

13

19

25

1

7

13

19

   

1

15

22

18

9

1

15

22

18

9

12

18

24

5

6

12

18

24

5

6

   

23

19

6

5

12

23

19

6

5

12

4

10

11

17

23

4

10

11

17

23

   

10

2

13

24

16

10

2

13

24

16

16

22

3

9

15

16

22

3

9

15

   

14

21

20

7

3

14

21

20

7

3

8

14

20

21

2

8

14

20

21

2

   

17

8

4

11

25

17

8

4

11

25

 


 Take 1x digit from first grid with 25x shifted version of the first panmagic 5x5 square

8

14

20

21

2

15

16

22

3

9

17

23

4

10

11

24

5

6

12

18

1

7

13

19

25

25

1

7

13

19

2

8

14

20

21

9

15

16

22

3

11

17

23

4

10

18

24

5

6

12

12

18

24

5

6

19

25

1

7

13

21

2

8

14

20

3

9

15

16

22

10

11

17

23

4

4

10

11

17

23

6

12

18

24

5

13

19

25

1

7

20

21

2

8

14

22

3

9

15

16

16

22

3

9

15

23

4

10

11

17

5

6

12

18

24

7

13

19

25

1

14

20

21

2

8

22

3

9

15

16

4

10

11

17

23

6

12

18

24

5

13

19

25

1

7

20

21

2

8

14

14

20

21

2

8

16

22

3

9

15

23

4

10

11

17

5

6

12

18

24

7

13

19

25

1

1

7

13

19

25

8

14

20

21

2

15

16

22

3

9

17

23

4

10

11

24

5

6

12

18

18

24

5

6

12

25

1

7

13

19

2

8

14

20

21

9

15

16

22

3

11

17

23

4

10

10

11

17

23

4

12

18

24

5

6

19

25

1

7

13

21

2

8

14

20

3

9

15

16

22

11

17

23

4

10

18

24

5

6

12

25

1

7

13

19

2

8

14

20

21

9

15

16

22

3

3

9

15

16

22

10

11

17

23

4

12

18

24

5

6

19

25

1

7

13

21

2

8

14

20

20

21

2

8

14

22

3

9

15

16

4

10

11

17

23

6

12

18

24

5

13

19

25

1

7

7

13

19

25

1

14

20

21

2

8

16

22

3

9

15

23

4

10

11

17

5

6

12

18

24

24

5

6

12

18

1

7

13

19

25

8

14

20

21

2

15

16

22

3

9

17

23

4

10

11

5

6

12

18

24

7

13

19

25

1

14

20

21

2

8

16

22

3

9

15

23

4

10

11

17

17

23

4

10

11

24

5

6

12

18

1

7

13

19

25

8

14

20

21

2

15

16

22

3

9

9

15

16

22

3

11

17

23

4

10

18

24

5

6

12

25

1

7

13

19

2

8

14

20

21

21

2

8

14

20

3

9

15

16

22

10

11

17

23

4

12

18

24

5

6

19

25

1

7

13

13

19

25

1

7

20

21

2

8

14

22

3

9

15

16

4

10

11

17

23

6

12

18

24

5

19

25

1

7

13

21

2

8

14

20

3

9

15

16

22

10

11

17

23

4

12

18

24

5

6

6

12

18

24

5

13

19

25

1

7

20

21

2

8

14

22

3

9

15

16

4

10

11

17

23

23

4

10

11

17

5

6

12

18

24

7

13

19

25

1

14

20

21

2

8

16

22

3

9

15

15

16

22

3

9

17

23

4

10

11

24

5

6

12

18

1

7

13

19

25

8

14

20

21

2

2

8

14

20

21

9

15

16

22

3

11

17

23

4

10

18

24

5

6

12

25

1

7

13

19

 

 

+ 25 x [digit -/- 1] from second grid with 25x shifted version of the second panmagic 5x5 sq.

17

8

4

11

25

21

20

7

3

14

13

24

16

10

2

5

12

23

19

6

9

1

15

22

18

1

15

22

18

9

8

4

11

25

17

20

7

3

14

21

24

16

10

2

13

12

23

19

6

5

23

19

6

5

12

15

22

18

9

1

4

11

25

17

8

7

3

14

21

20

16

10

2

13

24

10

2

13

24

16

19

6

5

12

23

22

18

9

1

15

11

25

17

8

4

3

14

21

20

7

14

21

20

7

3

2

13

24

16

10

6

5

12

23

19

18

9

1

15

22

25

17

8

4

11

15

22

18

9

1

4

11

25

17

8

7

3

14

21

20

16

10

2

13

24

23

19

6

5

12

19

6

5

12

23

22

18

9

1

15

11

25

17

8

4

3

14

21

20

7

10

2

13

24

16

2

13

24

16

10

6

5

12

23

19

18

9

1

15

22

25

17

8

4

11

14

21

20

7

3

21

20

7

3

14

13

24

16

10

2

5

12

23

19

6

9

1

15

22

18

17

8

4

11

25

8

4

11

25

17

20

7

3

14

21

24

16

10

2

13

12

23

19

6

5

1

15

22

18

9

6

5

12

23

19

18

9

1

15

22

25

17

8

4

11

14

21

20

7

3

2

13

24

16

10

13

24

16

10

2

5

12

23

19

6

9

1

15

22

18

17

8

4

11

25

21

20

7

3

14

20

7

3

14

21

24

16

10

2

13

12

23

19

6

5

1

15

22

18

9

8

4

11

25

17

4