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dekker.one
1/* -*- mode: C++; c-basic-offset: 2; indent-tabs-mode: nil -*- */
2/*
3 * Main authors:
4 * Christian Schulte <schulte@gecode.org>
5 *
6 * Contributing authors:
7 * Samuel Gagnon <samuel.gagnon92@gmail.com>
8
9 * Copyright:
10 * Christian Schulte, 2001
11 * Samuel Gagnon, 2018
12 *
13 * This file is part of Gecode, the generic constraint
14 * development environment:
15 * http://www.gecode.org
16 *
17 * Permission is hereby granted, free of charge, to any person obtaining
18 * a copy of this software and associated documentation files (the
19 * "Software"), to deal in the Software without restriction, including
20 * without limitation the rights to use, copy, modify, merge, publish,
21 * distribute, sublicense, and/or sell copies of the Software, and to
22 * permit persons to whom the Software is furnished to do so, subject to
23 * the following conditions:
24 *
25 * The above copyright notice and this permission notice shall be
26 * included in all copies or substantial portions of the Software.
27 *
28 * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
29 * EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF
30 * MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
31 * NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE
32 * LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION
33 * OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION
34 * WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.
35 *
36 */
37
38#include <gecode/driver.hh>
39#include <gecode/int.hh>
40#include <gecode/minimodel.hh>
41
42using namespace Gecode;
43
44namespace {
45 /// List of specifications
46 extern const int *specs[];
47 /// Number of specifications
48 extern const unsigned int n_examples;
49}
50
51/**
52 * \brief %Example: Magic squares
53 *
54 * Compute magic squares of arbitrary size
55 *
56 * See problem 19 at http://www.csplib.org/.
57 *
58 * \ingroup Example
59 *
60 */
61class MagicSquare : public Script {
62private:
63 /// Specification to be used
64 const int* spec;
65 /// Number of filled squares
66 const int n_filled;
67 /// Size of magic square
68 const int n;
69 /// Fields of square
70 IntVarArray x;
71
72public:
73 /// Branching to use for model
74 enum {
75 BRANCH_SIZE, ///< Branch by size
76 BRANCH_AFC_SIZE, ///< Branch by size over AFC
77 BRANCH_CBS_MAX_SD ///< Use maximum solution density
78 };
79 /// Post constraints
80 MagicSquare(const SizeOptions& opt)
81 : Script(opt), spec(specs[opt.size()]),
82 n_filled(spec[1]), n(spec[0]), x(*this,n*n,1,n*n) {
83 // Number of fields on square
84 const int nn = n*n;
85
86 // Sum of all a row, column, or diagonal
87 const int s = nn*(nn+1) / (2*n);
88
89 // Matrix-wrapper for the square
90 Matrix<IntVarArray> m(x, n, n);
91
92 for (int i=0; i<n_filled; i++) {
93 int row, col, num;
94 {
95 int idx = 3 * i + 2;
96 row = spec[idx] - 1;
97 col = spec[idx + 1] - 1;
98 num = spec[idx + 2];
99 }
100 rel(*this, m(col,row), IRT_EQ, num);
101 }
102
103 for (int i = n; i--; ) {
104 linear(*this, m.row(i), IRT_EQ, s, opt.ipl());
105 linear(*this, m.col(i), IRT_EQ, s, opt.ipl());
106 }
107 // Both diagonals must have sum s
108 {
109 IntVarArgs d1y(n);
110 IntVarArgs d2y(n);
111 for (int i = n; i--; ) {
112 d1y[i] = m(i,i);
113 d2y[i] = m(n-i-1,i);
114 }
115 linear(*this, d1y, IRT_EQ, s, opt.ipl());
116 linear(*this, d2y, IRT_EQ, s, opt.ipl());
117 }
118
119 // All fields must be distinct
120 distinct(*this, x, opt.ipl());
121
122 switch (opt.branching()) {
123 case BRANCH_CBS_MAX_SD:
124#ifdef GECODE_HAS_CBS
125 cbsbranch(*this, x);
126#endif
127 case BRANCH_SIZE:
128 branch(*this, x, INT_VAR_SIZE_MIN(), INT_VAL_SPLIT_MIN());
129 break;
130 case BRANCH_AFC_SIZE:
131 branch(*this, x, INT_VAR_AFC_SIZE_MAX(opt.decay()), INT_VAL_SPLIT_MIN());
132 break;
133 }
134 }
135
136 /// Constructor for cloning \a s
137 MagicSquare(MagicSquare& s)
138 : Script(s), spec(s.spec), n_filled(s.n_filled), n(s.n) {
139 x.update(*this, s.x);
140 }
141
142 /// Copy during cloning
143 virtual Space*
144 copy(void) {
145 return new MagicSquare(*this);
146 }
147 /// Print solution
148 virtual void
149 print(std::ostream& os) const {
150 // Matrix-wrapper for the square
151 Matrix<IntVarArray> m(x, n, n);
152 for (int i = 0; i<n; i++) {
153 os << "\t";
154 for (int j = 0; j<n; j++) {
155 os.width(2);
156 os << m(i,j) << " ";
157 }
158 os << std::endl;
159 }
160 }
161
162};
163
164/** \brief Main-function
165 * \relates MagicSquare
166 */
167int
168main(int argc, char* argv[]) {
169 SizeOptions opt("MagicSquare");
170 opt.iterations(1);
171 opt.size(0);
172 opt.branching(MagicSquare::BRANCH_SIZE);
173 opt.branching(MagicSquare::BRANCH_SIZE, "size");
174 opt.branching(MagicSquare::BRANCH_AFC_SIZE, "afc-size");
175#ifdef GECODE_HAS_CBS
176 opt.branching(MagicSquare::BRANCH_CBS_MAX_SD, "maxSD");
177#endif
178 opt.parse(argc,argv);
179 Script::run<MagicSquare,DFS,SizeOptions>(opt);
180 return 0;
181}
182
183namespace {
184
185 /** \name Magic-square specifications
186 *
187 * A specification is given by a list of integers. The first two integers (n
188 * and n_filled) specify the dimension of the magic square and the number of
189 * pre-filled square respectively. Then n_filled triplets <i, j, v> of
190 * integers follows, with i and j representing the row and the column of the
191 * value v.
192 *
193 * \relates Magic-square
194 */
195 //@{
196 const int magicSquare5_filled10_10[] = {
197 5,10,
198 1,2,18,
199 1,3,9,
200 1,5,2,
201 2,2,5,
202 3,1,1,
203 3,5,24,
204 4,2,21,
205 4,3,6,
206 5,2,13,
207 5,4,10,
208 };
209
210 const int magicSquare5_filled10_11[] = {
211 5,10,
212 1,3,6,
213 1,5,2,
214 2,2,8,
215 2,5,25,
216 3,1,1,
217 3,4,17,
218 3,5,24,
219 4,1,9,
220 4,2,21,
221 5,3,16,
222 };
223
224 const int magicSquare5_filled10_12[] = {
225 5,10,
226 1,2,5,
227 1,4,21,
228 2,1,10,
229 2,2,16,
230 2,3,8,
231 3,4,12,
232 4,2,20,
233 4,5,11,
234 5,1,18,
235 5,5,3,
236 };
237
238 const int magicSquare5_filled10_13[] = {
239 5,10,
240 1,5,2,
241 1,2,16,
242 2,3,8,
243 3,3,21,
244 3,1,1,
245 4,1,12,
246 5,2,6,
247 5,1,20,
248 5,3,14,
249 5,5,3,
250 };
251
252 const int magicSquare5_filled10_14[] = {
253 5,10,
254 1,3,14,
255 1,2,7,
256 2,3,12,
257 2,4,4,
258 3,3,21,
259 3,5,24,
260 4,5,11,
261 4,4,6,
262 4,3,13,
263 5,4,22,
264 };
265
266 const int magicSquare5_filled10_15[] = {
267 5,10,
268 1,5,2,
269 1,1,21,
270 2,1,15,
271 2,2,5,
272 4,2,18,
273 4,5,11,
274 5,4,20,
275 5,5,3,
276 5,2,12,
277 5,3,8,
278 };
279
280 const int magicSquare5_filled10_16[] = {
281 5,10,
282 1,1,22,
283 1,5,2,
284 1,4,18,
285 2,5,25,
286 2,4,7,
287 3,4,15,
288 3,1,1,
289 3,2,9,
290 4,4,4,
291 5,1,23,
292 };
293
294 const int magicSquare5_filled10_17[] = {
295 5,10,
296 1,2,5,
297 2,4,4,
298 2,5,25,
299 3,4,16,
300 3,5,24,
301 3,3,14,
302 3,1,1,
303 4,2,22,
304 5,3,13,
305 5,4,7,
306 };
307
308 const int magicSquare5_filled10_18[] = {
309 5,10,
310 1,3,7,
311 1,4,22,
312 2,5,25,
313 2,4,4,
314 2,1,10,
315 3,1,1,
316 4,4,6,
317 4,3,20,
318 5,3,8,
319 5,2,12,
320 };
321
322 const int magicSquare5_filled10_19[] = {
323 5,10,
324 1,2,6,
325 1,5,2,
326 2,2,18,
327 2,1,13,
328 3,5,24,
329 3,3,17,
330 5,2,7,
331 5,1,22,
332 5,4,21,
333 5,3,12,
334 };
335
336 const int magicSquare5_filled10_1[] = {
337 5,10,
338 1,4,16,
339 1,5,2,
340 1,3,20,
341 2,5,25,
342 2,4,4,
343 3,5,24,
344 3,1,1,
345 4,4,9,
346 5,2,12,
347 5,1,23,
348 };
349
350 const int magicSquare5_filled10_20[] = {
351 5,10,
352 1,1,22,
353 2,5,25,
354 2,2,5,
355 3,5,24,
356 3,1,1,
357 4,4,19,
358 4,5,11,
359 5,1,23,
360 5,2,8,
361 5,3,10,
362 };
363
364 const int magicSquare5_filled10_2[] = {
365 5,10,
366 1,2,19,
367 1,4,9,
368 2,5,25,
369 2,1,15,
370 3,2,6,
371 4,2,20,
372 4,1,5,
373 5,5,3,
374 5,3,10,
375 5,1,23,
376 };
377
378 const int magicSquare5_filled10_3[] = {
379 5,10,
380 1,1,15,
381 1,5,2,
382 2,1,20,
383 2,3,7,
384 3,4,5,
385 4,1,6,
386 4,4,16,
387 5,1,23,
388 5,2,12,
389 5,3,8,
390 };
391
392 const int magicSquare5_filled10_4[] = {
393 5,10,
394 1,2,15,
395 1,5,2,
396 1,1,22,
397 1,4,16,
398 2,5,25,
399 3,5,24,
400 3,1,1,
401 4,1,23,
402 4,2,18,
403 4,3,9,
404 };
405
406 const int magicSquare5_filled10_5[] = {
407 5,10,
408 1,1,14,
409 1,4,21,
410 2,2,12,
411 2,5,25,
412 3,2,5,
413 3,3,19,
414 3,5,24,
415 4,2,18,
416 5,1,22,
417 5,2,10,
418 };
419
420 const int magicSquare5_filled10_6[] = {
421 5,10,
422 1,1,19,
423 1,2,20,
424 2,1,7,
425 3,3,23,
426 4,5,11,
427 4,4,4,
428 5,3,13,
429 5,5,3,
430 5,4,22,
431 5,2,10,
432 };
433
434 const int magicSquare5_filled10_7[] = {
435 5,10,
436 1,2,10,
437 2,4,4,
438 3,5,24,
439 3,4,17,
440 4,5,11,
441 4,2,23,
442 4,4,5,
443 4,1,14,
444 5,2,6,
445 5,5,3,
446 };
447
448 const int magicSquare5_filled10_8[] = {
449 5,10,
450 1,1,22,
451 1,3,5,
452 2,5,25,
453 2,4,4,
454 3,5,24,
455 3,2,8,
456 4,1,10,
457 4,2,21,
458 4,3,16,
459 4,5,11,
460 };
461
462 const int magicSquare5_filled10_9[] = {
463 5,10,
464 1,5,2,
465 2,2,10,
466 2,5,25,
467 3,3,23,
468 3,1,1,
469 4,2,15,
470 4,4,13,
471 4,3,6,
472 5,5,3,
473 5,3,5,
474 };
475
476 const int magicSquare5_filled11_3_1[] = {
477 5,11,
478 1,1,15,
479 1,5,2,
480 2,1,20,
481 2,3,7,
482 3,2,13,
483 3,4,5,
484 4,1,6,
485 4,4,16,
486 5,1,23,
487 5,2,12,
488 5,3,8,
489 };
490
491 const int magicSquare5_filled11_5_1[] = {
492 5,11,
493 1,1,14,
494 1,4,21,
495 2,2,12,
496 2,5,25,
497 3,2,5,
498 3,3,19,
499 3,4,16,
500 3,5,24,
501 4,2,18,
502 5,1,22,
503 5,2,10,
504 };
505
506 const int magicSquare5_filled11_5_2[] = {
507 5,11,
508 1,1,14,
509 1,4,21,
510 2,2,12,
511 2,5,25,
512 3,2,5,
513 3,3,19,
514 3,5,24,
515 4,2,18,
516 5,1,22,
517 5,2,10,
518 5,5,3,
519 };
520
521 const int magicSquare5_filled11_5_3[] = {
522 5,11,
523 1,1,14,
524 1,3,8,
525 1,4,21,
526 2,2,12,
527 2,5,25,
528 3,2,5,
529 3,3,19,
530 3,5,24,
531 4,2,18,
532 5,1,22,
533 5,2,10,
534 };
535
536 const int magicSquare5_filled12_10_1[] = {
537 5,12,
538 1,2,18,
539 1,3,9,
540 1,5,2,
541 2,2,5,
542 3,1,1,
543 3,3,15,
544 3,5,24,
545 4,1,7,
546 4,2,21,
547 4,3,6,
548 5,2,13,
549 5,4,10,
550 };
551
552 const int magicSquare5_filled12_1_1[] = {
553 5,12,
554 1,1,21,
555 1,3,20,
556 1,4,16,
557 1,5,2,
558 2,5,25,
559 2,4,4,
560 3,1,1,
561 3,3,14,
562 3,5,24,
563 4,4,9,
564 5,2,12,
565 5,1,23,
566 };
567
568 const int magicSquare5_filled12_1_2[] = {
569 5,12,
570 1,3,20,
571 1,4,16,
572 1,5,2,
573 2,2,18,
574 2,4,4,
575 2,5,25,
576 3,1,1,
577 3,3,14,
578 3,5,24,
579 4,4,9,
580 5,2,12,
581 5,1,23,
582 };
583
584 const int magicSquare5_filled12_1_3[] = {
585 5,12,
586 1,3,20,
587 1,4,16,
588 1,5,2,
589 2,2,18,
590 2,4,4,
591 2,5,25,
592 3,1,1,
593 3,5,24,
594 4,4,9,
595 5,1,23,
596 5,2,12,
597 5,3,10,
598 };
599
600 const int magicSquare5_filled12_2_1[] = {
601 5,12,
602 1,1,21,
603 1,2,19,
604 1,4,9,
605 2,1,15,
606 2,5,25,
607 3,2,6,
608 3,4,18,
609 4,1,5,
610 4,2,20,
611 5,1,23,
612 5,3,10,
613 5,5,3,
614 };
615
616 const int magicSquare5_filled12_2_2[] = {
617 5,12,
618 1,2,19,
619 1,4,9,
620 2,1,15,
621 2,3,8,
622 2,5,25,
623 3,2,6,
624 3,4,18,
625 4,1,5,
626 4,2,20,
627 5,1,23,
628 5,3,10,
629 5,5,3,
630 };
631
632 const int magicSquare5_filled12_2_3[] = {
633 5,12,
634 1,1,21,
635 1,2,19,
636 1,4,9,
637 2,1,15,
638 2,5,25,
639 3,2,6,
640 4,1,5,
641 4,2,20,
642 4,4,12,
643 5,1,23,
644 5,3,10,
645 5,5,3,
646 };
647
648 const int magicSquare5_filled12_3_1[] = {
649 5,12,
650 1,1,15,
651 1,4,21,
652 1,5,2,
653 2,1,20,
654 2,3,7,
655 3,4,5,
656 4,1,6,
657 4,4,16,
658 5,1,23,
659 5,2,12,
660 5,3,8,
661 5,5,3,
662 };
663
664 const int magicSquare5_filled12_3_2[] = {
665 5,12,
666 1,1,15,
667 1,2,17,
668 1,3,10,
669 1,5,2,
670 2,1,20,
671 2,3,7,
672 3,4,5,
673 4,1,6,
674 4,4,16,
675 5,1,23,
676 5,2,12,
677 5,3,8,
678 };
679
680 const int magicSquare9_filled10_10[] = {
681 9,10,
682 8,2,19,
683 6,7,25,
684 7,3,15,
685 8,4,77,
686 7,1,29,
687 4,9,63,
688 4,6,53,
689 7,1,29,
690 3,9,36,
691 5,4,74,
692 };
693
694 const int magicSquare9_filled10_11[] = {
695 9,10,
696 5,5,78,
697 6,5,56,
698 9,8,30,
699 3,3,38,
700 2,3,9,
701 1,2,23,
702 3,5,80,
703 9,7,52,
704 7,5,1,
705 1,1,32,
706 };
707
708 const int magicSquare9_filled10_12[] = {
709 9,10,
710 6,7,25,
711 1,4,2,
712 5,1,54,
713 3,3,38,
714 7,2,71,
715 1,5,28,
716 3,2,50,
717 2,7,59,
718 7,7,42,
719 5,4,74,
720 };
721
722 const int magicSquare9_filled10_13[] = {
723 9,10,
724 7,2,71,
725 8,9,22,
726 2,2,17,
727 3,3,38,
728 1,8,72,
729 6,5,56,
730 5,6,41,
731 9,1,8,
732 7,8,37,
733 3,3,38,
734 };
735
736 const int magicSquare9_filled10_14[] = {
737 9,10,
738 9,4,35,
739 1,3,48,
740 9,6,69,
741 7,6,70,
742 6,1,46,
743 5,1,54,
744 4,2,62,
745 2,8,67,
746 7,6,70,
747 7,3,15,
748 };
749
750 const int magicSquare9_filled10_15[] = {
751 9,10,
752 9,8,30,
753 1,6,4,
754 9,9,45,
755 9,2,49,
756 5,6,41,
757 6,5,56,
758 5,9,7,
759 2,6,3,
760 3,2,50,
761 1,2,23,
762 };
763
764 const int magicSquare9_filled10_16[] = {
765 9,10,
766 1,9,81,
767 3,8,18,
768 8,4,77,
769 6,5,56,
770 7,9,31,
771 1,9,81,
772 7,3,15,
773 6,4,5,
774 6,8,61,
775 4,6,53,
776 };
777
778 const int magicSquare9_filled10_17[] = {
779 9,10,
780 4,4,12,
781 9,5,26,
782 7,6,70,
783 8,2,19,
784 7,2,71,
785 8,1,68,
786 8,2,19,
787 5,5,78,
788 6,3,21,
789 5,3,75,
790 };
791
792 const int magicSquare9_filled10_18[] = {
793 9,10,
794 7,2,71,
795 4,1,47,
796 6,9,24,
797 8,8,39,
798 3,9,36,
799 2,9,60,
800 4,3,64,
801 5,8,11,
802 4,2,62,
803 3,7,43,
804 };
805
806 const int magicSquare9_filled10_19[] = {
807 9,10,
808 7,4,73,
809 8,3,44,
810 8,1,68,
811 1,2,23,
812 1,6,4,
813 5,7,16,
814 3,6,6,
815 8,2,19,
816 4,5,14,
817 3,3,38,
818 };
819
820 const int magicSquare9_filled10_1[] = {
821 9,10,
822 4,5,14,
823 6,7,25,
824 8,8,39,
825 6,7,25,
826 3,8,18,
827 4,4,12,
828 8,2,19,
829 4,1,47,
830 4,6,53,
831 8,5,10,
832 };
833
834 const int magicSquare9_filled10_20[] = {
835 9,10,
836 1,4,2,
837 8,6,57,
838 1,5,28,
839 1,8,72,
840 6,1,46,
841 4,1,47,
842 8,7,33,
843 4,6,53,
844 1,5,28,
845 5,8,11,
846 };
847
848 const int magicSquare9_filled10_2[] = {
849 9,10,
850 2,5,76,
851 9,1,8,
852 2,4,51,
853 1,2,23,
854 9,7,52,
855 1,8,72,
856 3,3,38,
857 6,6,66,
858 3,7,43,
859 7,6,70,
860 };
861
862 const int magicSquare9_filled10_3[] = {
863 9,10,
864 5,6,41,
865 5,3,75,
866 6,1,46,
867 3,2,50,
868 3,8,18,
869 1,5,28,
870 3,2,50,
871 5,9,7,
872 4,8,34,
873 1,4,2,
874 };
875
876 const int magicSquare9_filled10_4[] = {
877 9,10,
878 4,9,63,
879 9,4,35,
880 7,5,1,
881 2,6,3,
882 8,4,77,
883 7,6,70,
884 5,8,11,
885 2,5,76,
886 9,4,35,
887 3,6,6,
888 };
889
890 const int magicSquare9_filled10_5[] = {
891 9,10,
892 2,5,76,
893 1,4,2,
894 9,3,55,
895 1,2,23,
896 3,3,38,
897 2,5,76,
898 3,4,40,
899 3,4,40,
900 1,2,23,
901 3,6,6,
902 };
903
904 const int magicSquare9_filled10_6[] = {
905 9,10,
906 7,5,1,
907 4,7,20,
908 8,7,33,
909 5,5,78,
910 5,2,13,
911 3,1,58,
912 1,9,81,
913 5,1,54,
914 3,1,58,
915 7,5,1,
916 };
917
918 const int magicSquare9_filled10_7[] = {
919 9,10,
920 7,5,1,
921 7,5,1,
922 1,5,28,
923 4,8,34,
924 4,1,47,
925 4,2,62,
926 2,6,3,
927 2,8,67,
928 1,9,81,
929 5,4,74,
930 };
931
932 const int magicSquare9_filled10_8[] = {
933 9,10,
934 9,4,35,
935 4,9,63,
936 1,6,4,
937 5,5,78,
938 7,5,1,
939 9,4,35,
940 5,6,41,
941 6,3,21,
942 9,3,55,
943 3,5,80,
944 };
945
946 const int magicSquare9_filled10_9[] = {
947 9,10,
948 4,8,34,
949 4,1,47,
950 3,9,36,
951 8,6,57,
952 9,2,49,
953 9,9,45,
954 1,6,4,
955 4,6,53,
956 3,6,6,
957 2,2,17,
958 };
959
960 const int magicSquare9_filled50_10[] = {
961 9,50,
962 4,3,64,
963 3,9,36,
964 8,3,44,
965 6,9,24,
966 2,7,59,
967 7,2,71,
968 8,2,19,
969 2,8,67,
970 6,7,25,
971 6,6,66,
972 3,8,18,
973 1,9,81,
974 8,4,77,
975 5,4,74,
976 8,2,19,
977 6,9,24,
978 4,9,63,
979 9,3,55,
980 2,5,76,
981 9,2,49,
982 3,7,43,
983 3,8,18,
984 6,3,21,
985 6,2,65,
986 9,2,49,
987 7,9,31,
988 8,6,57,
989 8,6,57,
990 9,3,55,
991 7,5,1,
992 2,4,51,
993 5,4,74,
994 3,4,40,
995 4,2,62,
996 6,3,21,
997 3,6,6,
998 7,4,73,
999 5,4,74,
1000 4,8,34,
1001 3,3,38,
1002 8,1,68,
1003 3,4,40,
1004 6,8,61,
1005 7,3,15,
1006 9,5,26,
1007 7,1,29,
1008 6,9,24,
1009 2,6,3,
1010 3,5,80,
1011 7,9,31,
1012 };
1013
1014 const int magicSquare9_filled50_11[] = {
1015 9,50,
1016 6,8,61,
1017 3,3,38,
1018 9,7,52,
1019 6,3,21,
1020 4,9,63,
1021 3,9,36,
1022 7,3,15,
1023 1,1,32,
1024 2,7,59,
1025 1,8,72,
1026 2,5,76,
1027 8,7,33,
1028 5,1,54,
1029 3,5,80,
1030 3,8,18,
1031 4,8,34,
1032 4,5,14,
1033 2,3,9,
1034 9,5,26,
1035 3,3,38,
1036 2,5,76,
1037 9,8,30,
1038 8,9,22,
1039 6,7,25,
1040 7,6,70,
1041 5,6,41,
1042 2,1,27,
1043 4,4,12,
1044 8,4,77,
1045 8,2,19,
1046 9,1,8,
1047 7,3,15,
1048 5,6,41,
1049 3,4,40,
1050 2,5,76,
1051 5,1,54,
1052 8,4,77,
1053 7,4,73,
1054 2,3,9,
1055 1,8,72,
1056 7,3,15,
1057 4,6,53,
1058 3,5,80,
1059 9,2,49,
1060 7,7,42,
1061 1,6,4,
1062 7,7,42,
1063 7,2,71,
1064 4,7,20,
1065 4,3,64,
1066 };
1067
1068 const int magicSquare9_filled50_12[] = {
1069 9,50,
1070 1,3,48,
1071 3,5,80,
1072 4,5,14,
1073 6,1,46,
1074 8,8,39,
1075 2,8,67,
1076 8,8,39,
1077 9,2,49,
1078 2,2,17,
1079 6,1,46,
1080 9,9,45,
1081 8,9,22,
1082 3,4,40,
1083 2,3,9,
1084 4,6,53,
1085 5,3,75,
1086 6,6,66,
1087 7,1,29,
1088 8,1,68,
1089 1,7,79,
1090 7,9,31,
1091 5,3,75,
1092 6,4,5,
1093 5,7,16,
1094 3,1,58,
1095 5,3,75,
1096 7,4,73,
1097 9,8,30,
1098 5,8,11,
1099 1,7,79,
1100 4,4,12,
1101 9,8,30,
1102 7,4,73,
1103 6,5,56,
1104 4,4,12,
1105 2,8,67,
1106 1,4,2,
1107 2,6,3,
1108 6,4,5,
1109 1,8,72,
1110 2,6,3,
1111 8,9,22,
1112 7,7,42,
1113 5,9,7,
1114 5,5,78,
1115 6,7,25,
1116 6,5,56,
1117 3,3,38,
1118 8,8,39,
1119 8,1,68,
1120 };
1121
1122 const int magicSquare9_filled50_13[] = {
1123 9,50,
1124 2,7,59,
1125 6,2,65,
1126 9,5,26,
1127 6,5,56,
1128 8,6,57,
1129 1,1,32,
1130 9,9,45,
1131 7,6,70,
1132 4,2,62,
1133 4,9,63,
1134 4,9,63,
1135 4,8,34,
1136 3,6,6,
1137 1,1,32,
1138 2,6,3,
1139 8,3,44,
1140 2,3,9,
1141 2,1,27,
1142 7,7,42,
1143 3,6,6,
1144 2,3,9,
1145 4,1,47,
1146 2,1,27,
1147 5,4,74,
1148 9,8,30,
1149 3,1,58,
1150 7,4,73,
1151 6,9,24,
1152 7,5,1,
1153 8,8,39,
1154 1,4,2,
1155 1,9,81,
1156 6,9,24,
1157 7,2,71,
1158 5,9,7,
1159 5,6,41,
1160 1,8,72,
1161 4,2,62,
1162 6,8,61,
1163 3,3,38,
1164 6,5,56,
1165 1,2,23,
1166 6,7,25,
1167 8,3,44,
1168 2,4,51,
1169 1,9,81,
1170 8,8,39,
1171 9,2,49,
1172 6,6,66,
1173 3,1,58,
1174 };
1175
1176 const int magicSquare9_filled50_14[] = {
1177 9,50,
1178 1,4,2,
1179 6,7,25,
1180 3,2,50,
1181 6,6,66,
1182 2,8,67,
1183 5,1,54,
1184 2,6,3,
1185 7,7,42,
1186 6,2,65,
1187 2,8,67,
1188 8,3,44,
1189 2,9,60,
1190 4,5,14,
1191 9,5,26,
1192 4,1,47,
1193 5,2,13,
1194 4,9,63,
1195 6,5,56,
1196 1,9,81,
1197 1,2,23,
1198 8,4,77,
1199 1,9,81,
1200 9,7,52,
1201 5,3,75,
1202 8,6,57,
1203 1,7,79,
1204 8,9,22,
1205 4,9,63,
1206 5,1,54,
1207 3,6,6,
1208 1,7,79,
1209 5,3,75,
1210 6,2,65,
1211 5,6,41,
1212 1,3,48,
1213 6,8,61,
1214 6,6,66,
1215 6,3,21,
1216 3,1,58,
1217 6,8,61,
1218 6,4,5,
1219 5,4,74,
1220 4,7,20,
1221 1,6,4,
1222 7,3,15,
1223 2,6,3,
1224 1,6,4,
1225 6,4,5,
1226 5,1,54,
1227 8,4,77,
1228 };
1229
1230 const int magicSquare9_filled50_15[] = {
1231 9,50,
1232 1,4,2,
1233 2,7,59,
1234 7,5,1,
1235 7,7,42,
1236 5,3,75,
1237 5,1,54,
1238 7,8,37,
1239 2,8,67,
1240 3,3,38,
1241 4,9,63,
1242 3,3,38,
1243 3,1,58,
1244 6,8,61,
1245 5,2,13,
1246 6,1,46,
1247 5,5,78,
1248 4,4,12,
1249 2,8,67,
1250 9,8,30,
1251 5,2,13,
1252 9,7,52,
1253 3,4,40,
1254 5,2,13,
1255 9,7,52,
1256 2,3,9,
1257 5,5,78,
1258 3,5,80,
1259 5,8,11,
1260 2,7,59,
1261 9,7,52,
1262 7,2,71,
1263 9,8,30,
1264 4,1,47,
1265 6,1,46,
1266 7,8,37,
1267 2,4,51,
1268 6,2,65,
1269 5,8,11,
1270 2,4,51,
1271 6,3,21,
1272 6,8,61,
1273 5,8,11,
1274 3,8,18,
1275 4,4,12,
1276 5,4,74,
1277 9,1,8,
1278 3,8,18,
1279 8,4,77,
1280 7,3,15,
1281 4,2,62,
1282 };
1283
1284 const int magicSquare9_filled50_16[] = {
1285 9,50,
1286 1,4,2,
1287 3,6,6,
1288 3,7,43,
1289 5,4,74,
1290 1,8,72,
1291 5,6,41,
1292 4,7,20,
1293 2,6,3,
1294 3,5,80,
1295 8,8,39,
1296 6,5,56,
1297 6,7,25,
1298 3,4,40,
1299 1,7,79,
1300 4,3,64,
1301 8,5,10,
1302 4,8,34,
1303 8,6,57,
1304 5,3,75,
1305 8,5,10,
1306 8,1,68,
1307 8,2,19,
1308 5,9,7,
1309 8,8,39,
1310 3,4,40,
1311 4,6,53,
1312 8,9,22,
1313 3,8,18,
1314 1,2,23,
1315 6,5,56,
1316 4,2,62,
1317 9,7,52,
1318 1,7,79,
1319 1,5,28,
1320 8,8,39,
1321 1,6,4,
1322 6,8,61,
1323 8,2,19,
1324 6,4,5,
1325 9,6,69,
1326 5,3,75,
1327 2,3,9,
1328 2,3,9,
1329 1,9,81,
1330 4,4,12,
1331 4,5,14,
1332 6,3,21,
1333 2,4,51,
1334 8,9,22,
1335 8,6,57,
1336 };
1337
1338 const int magicSquare9_filled50_17[] = {
1339 9,50,
1340 8,6,57,
1341 9,2,49,
1342 3,5,80,
1343 3,6,6,
1344 8,2,19,
1345 9,1,8,
1346 2,1,27,
1347 3,1,58,
1348 1,2,23,
1349 1,2,23,
1350 5,2,13,
1351 6,8,61,
1352 5,5,78,
1353 2,1,27,
1354 5,8,11,
1355 4,1,47,
1356 4,3,64,
1357 2,4,51,
1358 8,3,44,
1359 9,4,35,
1360 2,8,67,
1361 5,4,74,
1362 7,5,1,
1363 2,7,59,
1364 6,2,65,
1365 9,9,45,
1366 4,3,64,
1367 7,6,70,
1368 8,9,22,
1369 4,3,64,
1370 7,7,42,
1371 1,1,32,
1372 7,2,71,
1373 3,3,38,
1374 2,2,17,
1375 5,4,74,
1376 8,7,33,
1377 7,3,15,
1378 2,8,67,
1379 7,6,70,
1380 8,4,77,
1381 5,9,7,
1382 7,2,71,
1383 3,3,38,
1384 1,6,4,
1385 5,5,78,
1386 1,3,48,
1387 4,7,20,
1388 2,6,3,
1389 8,4,77,
1390 };
1391
1392 const int magicSquare9_filled50_18[] = {
1393 9,50,
1394 5,3,75,
1395 7,1,29,
1396 9,4,35,
1397 3,8,18,
1398 9,1,8,
1399 4,5,14,
1400 2,6,3,
1401 2,8,67,
1402 8,4,77,
1403 1,6,4,
1404 7,3,15,
1405 2,5,76,
1406 5,5,78,
1407 3,7,43,
1408 1,8,72,
1409 8,5,10,
1410 1,5,28,
1411 6,7,25,
1412 6,6,66,
1413 5,3,75,
1414 6,7,25,
1415 8,8,39,
1416 3,9,36,
1417 4,1,47,
1418 2,3,9,
1419 7,8,37,
1420 5,6,41,
1421 4,8,34,
1422 1,4,2,
1423 3,8,18,
1424 9,1,8,
1425 3,9,36,
1426 5,6,41,
1427 6,8,61,
1428 3,8,18,
1429 1,6,4,
1430 5,8,11,
1431 2,8,67,
1432 6,4,5,
1433 6,5,56,
1434 6,1,46,
1435 1,8,72,
1436 6,2,65,
1437 6,6,66,
1438 5,6,41,
1439 4,2,62,
1440 6,5,56,
1441 1,8,72,
1442 8,4,77,
1443 4,8,34,
1444 };
1445
1446 const int magicSquare9_filled50_19[] = {
1447 9,50,
1448 1,5,28,
1449 3,5,80,
1450 1,2,23,
1451 1,4,2,
1452 5,7,16,
1453 8,8,39,
1454 5,9,7,
1455 7,2,71,
1456 1,1,32,
1457 5,4,74,
1458 7,9,31,
1459 5,1,54,
1460 2,4,51,
1461 7,9,31,
1462 7,1,29,
1463 6,5,56,
1464 3,8,18,
1465 1,4,2,
1466 9,8,30,
1467 7,3,15,
1468 3,4,40,
1469 1,8,72,
1470 3,5,80,
1471 9,3,55,
1472 6,4,5,
1473 6,1,46,
1474 1,9,81,
1475 1,2,23,
1476 3,5,80,
1477 9,7,52,
1478 4,5,14,
1479 3,6,6,
1480 1,1,32,
1481 7,9,31,
1482 8,3,44,
1483 2,2,17,
1484 6,1,46,
1485 9,6,69,
1486 5,6,41,
1487 8,1,68,
1488 7,3,15,
1489 1,8,72,
1490 9,9,45,
1491 7,2,71,
1492 2,4,51,
1493 8,5,10,
1494 6,1,46,
1495 2,6,3,
1496 1,6,4,
1497 4,7,20,
1498 };
1499
1500 const int magicSquare9_filled50_1[] = {
1501 9,50,
1502 7,1,29,
1503 2,9,60,
1504 2,4,51,
1505 1,8,72,
1506 8,5,10,
1507 4,6,53,
1508 3,4,40,
1509 6,2,65,
1510 8,2,19,
1511 3,6,6,
1512 6,2,65,
1513 2,8,67,
1514 2,5,76,
1515 8,9,22,
1516 6,2,65,
1517 6,1,46,
1518 2,8,67,
1519 1,4,2,
1520 9,8,30,
1521 2,5,76,
1522 3,3,38,
1523 1,3,48,
1524 4,6,53,
1525 5,1,54,
1526 7,5,1,
1527 6,1,46,
1528 4,6,53,
1529 6,5,56,
1530 1,5,28,
1531 3,6,6,
1532 4,8,34,
1533 7,6,70,
1534 4,5,14,
1535 7,3,15,
1536 1,6,4,
1537 8,2,19,
1538 7,6,70,
1539 4,8,34,
1540 3,8,18,
1541 8,7,33,
1542 1,5,28,
1543 6,5,56,
1544 8,2,19,
1545 9,8,30,
1546 4,2,62,
1547 3,8,18,
1548 8,7,33,
1549 4,2,62,
1550 9,8,30,
1551 5,9,7,
1552 };
1553
1554 const int magicSquare9_filled50_20[] = {
1555 9,50,
1556 8,3,44,
1557 8,2,19,
1558 3,5,80,
1559 7,8,37,
1560 8,4,77,
1561 6,5,56,
1562 4,5,14,
1563 1,3,48,
1564 2,6,3,
1565 4,3,64,
1566 9,9,45,
1567 6,6,66,
1568 8,5,10,
1569 2,6,3,
1570 1,5,28,
1571 3,7,43,
1572 8,8,39,
1573 8,8,39,
1574 1,4,2,
1575 4,8,34,
1576 5,8,11,
1577 2,8,67,
1578 1,2,23,
1579 1,2,23,
1580 7,2,71,
1581 2,7,59,
1582 1,7,79,
1583 1,6,4,
1584 2,9,60,
1585 3,1,58,
1586 3,3,38,
1587 7,8,37,
1588 9,3,55,
1589 6,9,24,
1590 4,1,47,
1591 8,8,39,
1592 6,9,24,
1593 6,6,66,
1594 8,4,77,
1595 5,6,41,
1596 5,6,41,
1597 1,4,2,
1598 2,8,67,
1599 9,1,8,
1600 7,9,31,
1601 1,9,81,
1602 3,7,43,
1603 7,2,71,
1604 8,2,19,
1605 8,2,19,
1606 };
1607
1608 const int magicSquare9_filled50_2[] = {
1609 9,50,
1610 2,1,27,
1611 8,8,39,
1612 6,3,21,
1613 7,6,70,
1614 8,5,10,
1615 2,9,60,
1616 7,7,42,
1617 4,5,14,
1618 8,1,68,
1619 2,3,9,
1620 3,2,50,
1621 8,1,68,
1622 8,9,22,
1623 9,5,26,
1624 7,2,71,
1625 2,8,67,
1626 2,1,27,
1627 5,6,41,
1628 3,2,50,
1629 9,8,30,
1630 4,1,47,
1631 7,9,31,
1632 7,1,29,
1633 4,4,12,
1634 2,3,9,
1635 4,2,62,
1636 4,9,63,
1637 9,9,45,
1638 8,8,39,
1639 2,5,76,
1640 1,4,2,
1641 1,9,81,
1642 4,5,14,
1643 3,4,40,
1644 4,3,64,
1645 2,8,67,
1646 1,9,81,
1647 7,8,37,
1648 7,8,37,
1649 9,6,69,
1650 9,1,8,
1651 5,1,54,
1652 9,2,49,
1653 1,7,79,
1654 1,9,81,
1655 9,8,30,
1656 3,7,43,
1657 5,4,74,
1658 3,8,18,
1659 7,4,73,
1660 };
1661
1662 const int magicSquare9_filled50_3[] = {
1663 9,50,
1664 8,7,33,
1665 9,8,30,
1666 4,4,12,
1667 4,1,47,
1668 3,3,38,
1669 5,9,7,
1670 1,9,81,
1671 9,7,52,
1672 9,7,52,
1673 2,7,59,
1674 7,1,29,
1675 5,9,7,
1676 8,7,33,
1677 2,8,67,
1678 3,6,6,
1679 2,1,27,
1680 3,9,36,
1681 9,6,69,
1682 3,3,38,
1683 5,3,75,
1684 4,9,63,
1685 2,4,51,
1686 6,2,65,
1687 2,5,76,
1688 8,1,68,
1689 9,5,26,
1690 2,2,17,
1691 3,7,43,
1692 9,2,49,
1693 3,2,50,
1694 7,2,71,
1695 3,1,58,
1696 1,2,23,
1697 6,4,5,
1698 4,1,47,
1699 6,5,56,
1700 7,8,37,
1701 9,2,49,
1702 9,8,30,
1703 4,5,14,
1704 8,4,77,
1705 8,7,33,
1706 5,8,11,
1707 2,4,51,
1708 9,4,35,
1709 4,6,53,
1710 4,6,53,
1711 6,4,5,
1712 5,1,54,
1713 7,6,70,
1714 };
1715
1716 const int magicSquare9_filled50_4[] = {
1717 9,50,
1718 8,2,19,
1719 2,6,3,
1720 9,8,30,
1721 5,6,41,
1722 4,8,34,
1723 8,9,22,
1724 9,6,69,
1725 5,5,78,
1726 4,6,53,
1727 6,3,21,
1728 8,7,33,
1729 7,2,71,
1730 1,3,48,
1731 3,5,80,
1732 1,8,72,
1733 9,9,45,
1734 9,8,30,
1735 3,6,6,
1736 6,7,25,
1737 9,7,52,
1738 3,5,80,
1739 6,3,21,
1740 2,1,27,
1741 5,3,75,
1742 5,8,11,
1743 4,1,47,
1744 6,1,46,
1745 9,6,69,
1746 1,2,23,
1747 9,2,49,
1748 7,8,37,
1749 1,4,2,
1750 4,3,64,
1751 7,7,42,
1752 7,6,70,
1753 4,9,63,
1754 2,9,60,
1755 9,1,8,
1756 8,4,77,
1757 1,1,32,
1758 3,4,40,
1759 1,6,4,
1760 2,9,60,
1761 2,3,9,
1762 8,8,39,
1763 2,4,51,
1764 4,2,62,
1765 7,7,42,
1766 2,5,76,
1767 4,8,34,
1768 };
1769
1770 const int magicSquare9_filled50_5[] = {
1771 9,50,
1772 8,7,33,
1773 7,7,42,
1774 5,7,16,
1775 5,1,54,
1776 8,6,57,
1777 1,1,32,
1778 9,8,30,
1779 4,2,62,
1780 5,6,41,
1781 2,1,27,
1782 2,3,9,
1783 4,6,53,
1784 2,9,60,
1785 3,3,38,
1786 4,5,14,
1787 1,9,81,
1788 9,5,26,
1789 7,2,71,
1790 9,2,49,
1791 2,8,67,
1792 7,9,31,
1793 6,5,56,
1794 5,1,54,
1795 4,7,20,
1796 4,5,14,
1797 8,5,10,
1798 5,9,7,
1799 1,6,4,
1800 8,2,19,
1801 8,9,22,
1802 6,6,66,
1803 9,3,55,
1804 1,6,4,
1805 5,1,54,
1806 5,6,41,
1807 8,3,44,
1808 4,2,62,
1809 7,8,37,
1810 2,8,67,
1811 4,5,14,
1812 3,2,50,
1813 1,7,79,
1814 1,8,72,
1815 3,7,43,
1816 9,8,30,
1817 6,3,21,
1818 4,5,14,
1819 6,2,65,
1820 1,1,32,
1821 2,6,3,
1822 };
1823
1824 const int magicSquare9_filled50_6[] = {
1825 9,50,
1826 4,7,20,
1827 6,7,25,
1828 9,1,8,
1829 4,1,47,
1830 8,7,33,
1831 4,8,34,
1832 6,4,5,
1833 5,4,74,
1834 9,5,26,
1835 1,9,81,
1836 1,7,79,
1837 9,4,35,
1838 2,5,76,
1839 5,1,54,
1840 3,5,80,
1841 4,7,20,
1842 9,7,52,
1843 2,8,67,
1844 7,3,15,
1845 7,3,15,
1846 7,1,29,
1847 1,1,32,
1848 2,3,9,
1849 5,1,54,
1850 5,5,78,
1851 7,5,1,
1852 9,5,26,
1853 6,2,65,
1854 7,8,37,
1855 9,1,8,
1856 1,1,32,
1857 5,1,54,
1858 7,4,73,
1859 8,2,19,
1860 5,3,75,
1861 4,2,62,
1862 1,2,23,
1863 3,2,50,
1864 2,5,76,
1865 1,6,4,
1866 9,5,26,
1867 8,9,22,
1868 9,2,49,
1869 8,5,10,
1870 9,5,26,
1871 5,1,54,
1872 5,7,16,
1873 8,2,19,
1874 1,4,2,
1875 3,3,38,
1876 };
1877
1878 const int magicSquare9_filled50_7[] = {
1879 9,50,
1880 6,3,21,
1881 7,6,70,
1882 3,4,40,
1883 5,2,13,
1884 6,6,66,
1885 7,8,37,
1886 8,6,57,
1887 8,1,68,
1888 2,9,60,
1889 4,8,34,
1890 7,3,15,
1891 2,3,9,
1892 4,3,64,
1893 2,2,17,
1894 7,2,71,
1895 3,3,38,
1896 4,9,63,
1897 8,4,77,
1898 2,4,51,
1899 3,5,80,
1900 7,1,29,
1901 3,5,80,
1902 6,1,46,
1903 4,7,20,
1904 1,5,28,
1905 3,5,80,
1906 8,4,77,
1907 7,2,71,
1908 6,8,61,
1909 3,3,38,
1910 8,4,77,
1911 3,9,36,
1912 1,2,23,
1913 4,2,62,
1914 3,6,6,
1915 4,7,20,
1916 4,7,20,
1917 9,9,45,
1918 5,1,54,
1919 4,3,64,
1920 6,6,66,
1921 8,2,19,
1922 8,5,10,
1923 3,2,50,
1924 2,4,51,
1925 3,7,43,
1926 5,5,78,
1927 4,5,14,
1928 4,7,20,
1929 5,4,74,
1930 };
1931
1932 const int magicSquare9_filled50_8[] = {
1933 9,50,
1934 2,8,67,
1935 1,3,48,
1936 5,8,11,
1937 3,8,18,
1938 8,6,57,
1939 1,2,23,
1940 1,8,72,
1941 3,8,18,
1942 2,4,51,
1943 7,1,29,
1944 5,9,7,
1945 5,9,7,
1946 5,8,11,
1947 4,6,53,
1948 4,8,34,
1949 1,3,48,
1950 5,8,11,
1951 5,7,16,
1952 6,5,56,
1953 5,3,75,
1954 9,4,35,
1955 4,9,63,
1956 9,5,26,
1957 5,8,11,
1958 8,2,19,
1959 6,3,21,
1960 9,1,8,
1961 2,4,51,
1962 7,3,15,
1963 9,1,8,
1964 9,7,52,
1965 1,2,23,
1966 6,5,56,
1967 8,2,19,
1968 8,2,19,
1969 2,7,59,
1970 5,6,41,
1971 6,4,5,
1972 8,8,39,
1973 3,6,6,
1974 7,8,37,
1975 6,6,66,
1976 7,5,1,
1977 7,2,71,
1978 5,5,78,
1979 2,2,17,
1980 2,9,60,
1981 3,7,43,
1982 2,2,17,
1983 7,9,31,
1984 };
1985
1986 const int magicSquare9_filled50_9[] = {
1987 9,50,
1988 3,8,18,
1989 6,7,25,
1990 2,9,60,
1991 8,9,22,
1992 7,8,37,
1993 3,3,38,
1994 5,6,41,
1995 8,2,19,
1996 8,4,77,
1997 3,4,40,
1998 8,2,19,
1999 5,9,7,
2000 8,8,39,
2001 5,9,7,
2002 7,9,31,
2003 9,9,45,
2004 5,5,78,
2005 4,7,20,
2006 3,9,36,
2007 4,9,63,
2008 8,5,10,
2009 9,3,55,
2010 8,6,57,
2011 2,7,59,
2012 9,2,49,
2013 1,7,79,
2014 1,3,48,
2015 4,8,34,
2016 8,6,57,
2017 7,5,1,
2018 5,6,41,
2019 2,1,27,
2020 9,3,55,
2021 5,2,13,
2022 3,6,6,
2023 8,1,68,
2024 8,8,39,
2025 1,7,79,
2026 2,2,17,
2027 4,1,47,
2028 1,2,23,
2029 5,1,54,
2030 2,6,3,
2031 8,1,68,
2032 3,5,80,
2033 3,5,80,
2034 9,3,55,
2035 3,8,18,
2036 5,7,16,
2037 7,5,1,
2038 };
2039
2040 const int *specs[] = {
2041 magicSquare5_filled10_1, //0
2042 magicSquare5_filled10_2, //1
2043 magicSquare5_filled10_3, //2
2044 magicSquare5_filled10_4, //3
2045 magicSquare5_filled10_5, //4
2046 magicSquare5_filled10_6, //5
2047 magicSquare5_filled10_7, //6
2048 magicSquare5_filled10_8, //7
2049 magicSquare5_filled10_9, //8
2050 magicSquare5_filled10_10, //9
2051 magicSquare5_filled10_11, //10
2052 magicSquare5_filled10_12, //11
2053 magicSquare5_filled10_13, //12
2054 magicSquare5_filled10_14, //13
2055 magicSquare5_filled10_15, //14
2056 magicSquare5_filled10_16, //15
2057 magicSquare5_filled10_17, //16
2058 magicSquare5_filled10_18, //17
2059 magicSquare5_filled10_19, //18
2060 magicSquare5_filled10_20, //19
2061 magicSquare5_filled11_3_1, //20
2062 magicSquare5_filled11_5_1, //21
2063 magicSquare5_filled11_5_2, //22
2064 magicSquare5_filled11_5_3, //23
2065 magicSquare5_filled12_10_1, //24
2066 magicSquare5_filled12_1_1, //25
2067 magicSquare5_filled12_1_2, //26
2068 magicSquare5_filled12_1_3, //27
2069 magicSquare5_filled12_2_1, //28
2070 magicSquare5_filled12_2_2, //29
2071 magicSquare5_filled12_2_3, //30
2072 magicSquare5_filled12_3_1, //31
2073 magicSquare5_filled12_3_2, //32
2074 magicSquare9_filled10_1, //33
2075 magicSquare9_filled10_2, //34
2076 magicSquare9_filled10_3, //35
2077 magicSquare9_filled10_4, //36
2078 magicSquare9_filled10_5, //37
2079 magicSquare9_filled10_6, //38
2080 magicSquare9_filled10_7, //39
2081 magicSquare9_filled10_8, //40
2082 magicSquare9_filled10_9, //41
2083 magicSquare9_filled10_10, //42
2084 magicSquare9_filled10_11, //43
2085 magicSquare9_filled10_12, //44
2086 magicSquare9_filled10_13, //45
2087 magicSquare9_filled10_14, //46
2088 magicSquare9_filled10_15, //47
2089 magicSquare9_filled10_16, //48
2090 magicSquare9_filled10_17, //49
2091 magicSquare9_filled10_18, //50
2092 magicSquare9_filled10_19, //51
2093 magicSquare9_filled10_20, //52
2094 magicSquare9_filled50_1, //53
2095 magicSquare9_filled50_2, //54
2096 magicSquare9_filled50_3, //55
2097 magicSquare9_filled50_4, //56
2098 magicSquare9_filled50_5, //57
2099 magicSquare9_filled50_6, //58
2100 magicSquare9_filled50_7, //59
2101 magicSquare9_filled50_8, //60
2102 magicSquare9_filled50_9, //61
2103 magicSquare9_filled50_10, //62
2104 magicSquare9_filled50_11, //63
2105 magicSquare9_filled50_12, //64
2106 magicSquare9_filled50_13, //65
2107 magicSquare9_filled50_14, //66
2108 magicSquare9_filled50_15, //67
2109 magicSquare9_filled50_16, //68
2110 magicSquare9_filled50_17, //69
2111 magicSquare9_filled50_18, //70
2112 magicSquare9_filled50_19, //71
2113 magicSquare9_filled50_20 //72
2114 };
2115
2116 const unsigned n_examples = sizeof(specs)/sizeof(int*);
2117 //@}
2118
2119}
2120
2121// STATISTICS: example-any
2122