Â
Harm Derksen introduced on his website http://www.math.lsa.umich.edu/~hderksen/magic.html an 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 number x number instead of
each number and each row/column/diagonal gives the bimagic sum of 3263025.
Use 2x the same or 2 different panmagic 5x5 squares to construct the 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 |
Â
 Take 1x number 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 |
Â
Â
+ 25 x [number -/- 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 |
|