Bimagic 25x25 square
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 |
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 |
+ 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 |
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 |
11 |
25 |
17 |
8 |
7 |
3 |
14 |
21 |
20 |
16 |
10 |
2 |
13 |
24 |
23 |
19 |
6 |
5 |
12 |
15 |
22 |
18 |
9 |
1 |
|
22 |
18 |
9 |
1 |
15 |
11 |
25 |
17 |
8 |
4 |
3 |
14 |
21 |
20 |
7 |
10 |
2 |
13 |
24 |
16 |
19 |
6 |
5 |
12 |
23 |
|
24 |
16 |
10 |
2 |
13 |
12 |
23 |
19 |
6 |
5 |
1 |
15 |
22 |
18 |
9 |
8 |
4 |
11 |
25 |
17 |
20 |
7 |
3 |
14 |
21 |
|
7 |
3 |
14 |
21 |
20 |
16 |
10 |
2 |
13 |
24 |
23 |
19 |
6 |
5 |
12 |
15 |
22 |
18 |
9 |
1 |
4 |
11 |
25 |
17 |
8 |
|
11 |
25 |
17 |
8 |
4 |
3 |
14 |
21 |
20 |
7 |
10 |
2 |
13 |
24 |
16 |
19 |
6 |
5 |
12 |
23 |
22 |
18 |
9 |
1 |
15 |
|
18 |
9 |
1 |
15 |
22 |
25 |
17 |
8 |
4 |
11 |
14 |
21 |
20 |
7 |
3 |
2 |
13 |
24 |
16 |
10 |
6 |
5 |
12 |
23 |
19 |
|
5 |
12 |
23 |
19 |
6 |
9 |
1 |
15 |
22 |
18 |
17 |
8 |
4 |
11 |
25 |
21 |
20 |
7 |
3 |
14 |
13 |
24 |
16 |
10 |
2 |
|
3 |
14 |
21 |
20 |
7 |
10 |
2 |
13 |
24 |
16 |
19 |
6 |
5 |
12 |
23 |
22 |
18 |
9 |
1 |
15 |
11 |
25 |
17 |
8 |
4 |
|
25 |
17 |
8 |
4 |
11 |
14 |
21 |
20 |
7 |
3 |
2 |
13 |
24 |
16 |
10 |
6 |
5 |
12 |
23 |
19 |
18 |
9 |
1 |
15 |
22 |
|
9 |
1 |
15 |
22 |
18 |
17 |
8 |
4 |
11 |
25 |
21 |
20 |
7 |
3 |
14 |
13 |
24 |
16 |
10 |
2 |
5 |
12 |
23 |
19 |
6 |
|
12 |
23 |
19 |
6 |
5 |
1 |
15 |
22 |
18 |
9 |
8 |
4 |
11 |
25 |
17 |
20 |
7 |
3 |
14 |
21 |
24 |
16 |
10 |
2 |
13 |
|
16 |
10 |
2 |
13 |
24 |
23 |
19 |
6 |
5 |
12 |
15 |
22 |
18 |
9 |
1 |
4 |
11 |
25 |
17 |
8 |
7 |
3 |
14 |
21 |
20 |
Bimagic 25x25 square
|
408 |
189 |
95 |
271 |
602 |
515 |
491 |
172 |
53 |
334 |
317 |
598 |
379 |
235 |
36 |
124 |
280 |
556 |
462 |
143 |
201 |
7 |
363 |
544 |
450 |
|
25 |
351 |
532 |
438 |
219 |
177 |
83 |
264 |
620 |
421 |
484 |
165 |
66 |
347 |
503 |
586 |
392 |
248 |
29 |
310 |
293 |
574 |
455 |
131 |
112 |
|
562 |
468 |
149 |
105 |
281 |
369 |
550 |
426 |
207 |
13 |
96 |
252 |
608 |
414 |
195 |
153 |
59 |
340 |
516 |
497 |
385 |
236 |
42 |
323 |
579 |
|
229 |
35 |
311 |
592 |
398 |
456 |
137 |
118 |
299 |
555 |
538 |
444 |
225 |
1 |
357 |
270 |
621 |
402 |
183 |
89 |
72 |
328 |
509 |
490 |
166 |
|
341 |
522 |
478 |
159 |
65 |
48 |
304 |
585 |
386 |
242 |
130 |
106 |
287 |
568 |
474 |
432 |
213 |
19 |
375 |
526 |
614 |
420 |
196 |
77 |
258 |
|
372 |
528 |
434 |
215 |
16 |
79 |
260 |
611 |
417 |
198 |
156 |
62 |
343 |
524 |
480 |
388 |
244 |
50 |
301 |
582 |
570 |
471 |
127 |
108 |
289 |
|
464 |
145 |
121 |
277 |
558 |
541 |
447 |
203 |
9 |
365 |
273 |
604 |
410 |
186 |
92 |
55 |
331 |
512 |
493 |
174 |
232 |
38 |
319 |
600 |
376 |
|
26 |
307 |
588 |
394 |
250 |
133 |
114 |
295 |
571 |
452 |
440 |
216 |
22 |
353 |
534 |
617 |
423 |
179 |
85 |
261 |
349 |
505 |
481 |
162 |
68 |
|
518 |
499 |
155 |
56 |
337 |
325 |
576 |
382 |
238 |
44 |
102 |
283 |
564 |
470 |
146 |
209 |
15 |
366 |
547 |
428 |
411 |
192 |
98 |
254 |
610 |
|
185 |
86 |
267 |
623 |
404 |
487 |
168 |
74 |
330 |
506 |
594 |
400 |
226 |
32 |
313 |
296 |
552 |
458 |
139 |
120 |
3 |
359 |
540 |
441 |
222 |
|
136 |
117 |
298 |
554 |
460 |
443 |
224 |
5 |
356 |
537 |
625 |
401 |
182 |
88 |
269 |
327 |
508 |
489 |
170 |
71 |
34 |
315 |
591 |
397 |
228 |
|
303 |
584 |
390 |
241 |
47 |
110 |
286 |
567 |
473 |
129 |
212 |
18 |
374 |
530 |
431 |
419 |
200 |
76 |
257 |
613 |
521 |
477 |
158 |
64 |
345 |
|
495 |
171 |
52 |
333 |
514 |
597 |
378 |
234 |
40 |
316 |
279 |
560 |
461 |
142 |
123 |
6 |
362 |
543 |
449 |
205 |
188 |
94 |
275 |
601 |
407 |
|
82 |
263 |
619 |
425 |
176 |
164 |
70 |
346 |
502 |
483 |
391 |
247 |
28 |
309 |
590 |
573 |
454 |
135 |
111 |
292 |
355 |
531 |
437 |
218 |
24 |
|
549 |
430 |
206 |
12 |
368 |
251 |
607 |
413 |
194 |
100 |
58 |
339 |
520 |
496 |
152 |
240 |
41 |
322 |
578 |
384 |
467 |
148 |
104 |
285 |
561 |
|
580 |
381 |
237 |
43 |
324 |
282 |
563 |
469 |
150 |
101 |
14 |
370 |
546 |
427 |
208 |
191 |
97 |
253 |
609 |
415 |
498 |
154 |
60 |
336 |
517 |
|
167 |
73 |
329 |
510 |
486 |
399 |
230 |
31 |
312 |
593 |
551 |
457 |
138 |
119 |
300 |
358 |
539 |
445 |
221 |
2 |
90 |
266 |
622 |
403 |
184 |
|
259 |
615 |
416 |
197 |
78 |
61 |
342 |
523 |
479 |
160 |
243 |
49 |
305 |
581 |
387 |
475 |
126 |
107 |
288 |
569 |
527 |
433 |
214 |
20 |
371 |
|
446 |
202 |
8 |
364 |
545 |
603 |
409 |
190 |
91 |
272 |
335 |
511 |
492 |
173 |
54 |
37 |
318 |
599 |
380 |
231 |
144 |
125 |
276 |
557 |
463 |
|
113 |
294 |
575 |
451 |
132 |
220 |
21 |
352 |
533 |
439 |
422 |
178 |
84 |
265 |
616 |
504 |
485 |
161 |
67 |
348 |
306 |
587 |
393 |
249 |
30 |
|
69 |
350 |
501 |
482 |
163 |
246 |
27 |
308 |
589 |
395 |
453 |
134 |
115 |
291 |
572 |
535 |
436 |
217 |
23 |
354 |
262 |
618 |
424 |
180 |
81 |
|
606 |
412 |
193 |
99 |
255 |
338 |
519 |
500 |
151 |
57 |
45 |
321 |
577 |
383 |
239 |
147 |
103 |
284 |
565 |
466 |
429 |
210 |
11 |
367 |
548 |
|
223 |
4 |
360 |
536 |
442 |
405 |
181 |
87 |
268 |
624 |
507 |
488 |
169 |
75 |
326 |
314 |
595 |
396 |
227 |
33 |
116 |
297 |
553 |
459 |
140 |
|
290 |
566 |
472 |
128 |
109 |
17 |
373 |
529 |
435 |
211 |
199 |
80 |
256 |
612 |
418 |
476 |
157 |
63 |
344 |
525 |
583 |
389 |
245 |
46 |
302 |
|
377 |
233 |
39 |
320 |
596 |
559 |
465 |
141 |
122 |
278 |
361 |
542 |
448 |
204 |
10 |
93 |
274 |
605 |
406 |
187 |
175 |
51 |
332 |
513 |
494 |
