ORDER-4 MAGIC SQUARES GROUPED BY BASE SQUARE QUARTETS

The 880 numbered Frénicle order-4 magic squares are listed below in groups that are derived from the same base square quartet(s). (A base square [or base square set for catchup base square sets] and its complement are treated as the same base square in this discussion, i.e. C2 and C6 are interchangeable as are the catchup pairs F3:E20 and F19:E4.) There are four major divisions of the magic squares on this page. The first division of squares use only base squares with main diagonals that are predictable. The second division of magic squares have two base squares that use catchup in their main diagonals, the other two base squares are predictable. Squares in the third division have three base squares using catchup and in the fourth division all the base squares use catchup for their main diagonals.

In the first two divisions the magic squares in each column are made from the base square quartets given at the top of the column. There can be one, two, or four sets of base square quartets that yield the same group of magic squares after transformations using Frénicle's rules. The base square quartet(s) that generate the group of magic squares are given at the top of each column. Below the base square quartet listing is the number of magic squares that are derived from the base square quartet(s).

If the magic square group has any commonly recognized feature(s), they are listed below the number of magic squares. Below that are the classifications of that group according to Walkington and Dudeney.

Directly above the actual listing of magic squares are squares that show Walkington's sub-magic 2x2 square patterns or transpose of those patterns for all group members. A number 34 indicates a sub-magic 2x2 square with the 34 placed in its upper left corner. The numbers in that 2x2 square sum to 34. If a 2x2 square does not sum to the magic constant, there is no number present in its upper left corner. If all 16 sub squares sum to 34, the magic square is compact2. Numbers in the right column and bottom row require the pan property to complete the 2x2 sub square. The bottom right corner corresponds to the sum of the four corners of the magic square. The orientation of the sub square pattern in a Frénicle magic square will often be different than the orientation shown.

In the last two divisions of the table there are 28 and 24 groups of four and two magic squares respectively. Only eight columns are shown so the tables are split into 4 and 3 sub sections respectively. Each sub section has headings for the magic squares in that sub section.

ORTHODOX MAGIC SQUARES

The first three columns of orthodox magic squares are defined by just one base square quartet given in the header (In the base square quartets a base square can be the base square listed or its complement, i.e. B3+C1+F1+F2 should be read as either B3 or B7 and either C1 or C5 and either F1 or F16 and either F2 or F17.). In the last four groups of magic squares, 2 base square quartets generate the same group of Frénicle order-4 magic squares. This is because the 2 base square quartets can be interconverted by a simple transformation of all four base squares. A more detailed description of the features of each group is given in ORTHODOX ORDER-4 MAGIC SQUARES. A discussion of those features presence in base squares is given in Order-4 Magic Square Features.

Orthodox Order-4 Magic Squares
Orthodox Group 1
B1+B2+B3+B4

48 squares
pan diagonal
compact_2,3
complete
Walkington T4.01
Dudeney Group I
2x2 sub-square pattern
34343434
34343434
34343434
34343434
Orthodox Group 2
B1+B2+C1+C2

48 squares
semi-pan diagonal
compact_3

Walkington T4.02.2
Dudeney Group II
2x2 sub-square pattern
3434
3434
3434
3434
Orthodox Group 3
B3+B4+C1+C2

48 squares
semi-pan diagonal
compact_3
associated
Walkington T4.02.2
Dudeney Group III
2x2 sub-square pattern
3434
3434
3434
3434
Orthodox Group 4
B1+B3+B4+C1
B2+B3+B4+C2
96 squares
semi-pan diagonal
compact_3

Walkington T4.02.1
Dudeney Group IV
2x2 sub-square pattern
34343434
3434
34343434
3434
Orthodox Group 5
B1+B4+C1+C2
B2+B3+C1+C2
96 squares
semi-pan diagonal
compact_3

Walkington T4.02.3
Dudeney Group V
2x2 sub-square pattern
3434
3434
3434
3434
Orthodox Group 6
B1+B2+B3+C1
B1+B2+B4+C2
96 squares
semi-pan diagonal
compact_3

Walkington T4.02.1
Dudeney Group VI
2x2 sub-square pattern
34343434
3434
34343434
3434
Orthodox Group 7
B3+C1+F1+F2
B4+C2+F1+F2
96 squares
88 simple
Walkington T4.05.1
8 part.pan diagonal
Walkington T4.03.1
Dudeney Group VI
2x2 sub-square pattern
3434
3434
3434
3434
102
181015
121336
72169
141154
21
141415
131623
851110
12976
112
181213
141172
151063
45916
24
141415
161332
76129
101158
32
141613
141532
761011
12958
16
141316
141523
85129
111076
12
141316
81439
155122
101167
104
181015
141154
72169
121336
22
141415
131623
12976
851110
113
181213
151063
141172
45916
25
141415
161332
111085
67912
33
141613
141532
111067
85912
17
141316
141523
12985
761110
13
141316
81529
145123
111076
107
181114
121327
63169
151054
27
141514
131632
851011
12967
120
181411
121372
151045
63916
30
141514
161323
67129
111058
34
141613
151423
671110
12958
18
141316
151432
85129
101167
14
141316
121435
15982
671011
109
181114
151054
63169
121327
28
141514
131632
12967
851011
122
181411
151045
121372
63916
31
141514
161323
101185
76912
35
141613
151423
101176
85912
19
141316
151432
12985
671011
15
141316
121525
14983
761110
116
181312
141127
45169
151036
56
161215
111625
831310
14974
124
181510
121363
141145
72916
60
161215
161152
74149
101338
66
161611
121552
741013
14938
48
161116
121525
83149
131074
45
161116
81259
153142
101347
117
181312
151036
45169
141127
57
161215
111625
14974
831310
126
181510
141145
121363
72916
61
161215
161152
131083
47914
67
161611
121552
131047
83914
49
161116
121525
14983
741310
46
161116
81529
123145
131074
171
112615
14794
112165
813310
62
161512
111652
831013
14947
175
112813
147112
156103
49516
64
161512
161125
47149
131038
68
161611
151225
471310
14938
54
161116
151252
83149
101347
51
161116
141253
15982
471013
174
112714
15694
103165
813211
63
161512
111652
14947
831013
176
112813
156103
147112
49516
65
161512
161125
101383
74914
69
161611
151225
101374
83914
55
161116
151252
14983
471013
53
161116
141523
12985
741310
177
112138
147211
49165
156310
82
171214
101635
821311
15964
183
112147
15649
813112
103516
84
171214
161053
64159
111328
95
171610
121453
641113
15928
73
171016
121435
82159
131164
70
171016
81259
142153
111346
178
112138
156310
49165
147211
83
171214
101635
15964
821311
185
112156
14749
813103
112516
85
171214
161053
131182
46915
96
171610
121453
131146
82915
74
171016
121435
15982
641311
71
171016
81439
122155
131164
201
114712
15496
105163
811213
89
171412
101653
821113
15946
203
114811
154105
127132
69316
92
171412
161035
46159
131128
97
171610
141235
461311
15928
76
171016
141253
82159
111346
80
171016
151252
14983
461113
204
114118
154510
69163
127213
90
171412
101653
15946
821113
206
114127
15469
811132
105316
93
171412
161035
111382
64915
98
171610
141235
111364
82915
77
171016
141253
15982
461113
81
171016
151432
12985
641311
279
27916
111445
811510
131263
213
231316
141514
76129
111085
289
271114
131281
16954
361015
140
110815
16792
114145
613312
101
181015
111445
16972
631312
110
181213
101536
721411
16954
130
110716
12895
153142
613411
281
27916
131263
811510
111445
214
231316
141514
111085
76129
290
271114
16954
131281
361015
141
110815
16792
136123
411514
103
181015
131263
16972
451114
111
181213
111427
631510
16954
132
110716
121525
83149
136114
292
271213
111418
541510
16963
233
231613
141541
76912
111058
297
271312
111481
16936
541015
146
110158
16729
411145
136312
106
181114
101545
16963
721312
119
181411
101554
721213
16936
133
110716
14893
155122
411613
294
271213
16963
541510
111418
234
231613
141541
111058
76912
299
271312
16936
111481
541015
147
110158
16729
613123
114514
108
181114
131272
16963
451015
121
181411
131227
451510
16936
135
110716
141523
85129
114136
304
271411
131218
361510
16945
246
251116
121516
74149
131083
306
27169
111454
131236
811015
159
111814
16693
104155
713212
114
181312
101563
16945
721114
123
181510
111454
631213
16927
150
111616
12895
142153
713410
305
271411
16945
361510
131218
247
251116
121516
131083
74149
308
27169
131236
111454
811015
160
111814
16693
137122
410515
115
181312
111472
16945
631015
125
181510
131236
451411
16927
151
111616
121435
82159
137104
355
211516
138103
121156
71449
269
251611
121561
74914
131038
360
211714
138121
16594
310615
162
111148
16639
410155
137212
148
110167
15829
411136
145312
136
110716
15892
123145
613411
157
111616
15892
145123
410713
365
211813
165103
94156
714112
270
251611
121561
131038
74914
361
211714
16594
138121
310615
163
111148
16639
713122
104515
149
110167
15829
613114
123514
137
110716
15892
145123
411613
158
111616
151432
85129
104137
372
211147
138112
310156
16549
316
281113
91546
711412
161053
368
211138
165310
714121
94615
191
113812
16495
106153
711214
164
111166
14839
410137
155212
154
111616
14893
122155
713410
187
113416
14893
122155
711610
375
211147
16549
310156
138112
317
281113
91546
161053
711412
377
211165
138310
71494
121615
192
113812
16495
117142
610315
165
111166
14839
713104
122515
155
111616
14893
155122
410713
188
113416
141253
82159
117106
393
213811
163105
96154
712114
323
281311
91564
711214
161035
392
213712
16396
118141
510415
195
113128
16459
610153
117214
169
112615
138103
165112
49714
182
112147
138211
49156
165310
189
113416
15892
123145
610711
396
213127
16369
510154
118114
324
281311
91564
161035
711214
395
213118
163510
712141
96415
196
113128
16459
711142
106315
173
112714
138112
165103
49615
184
112156
138310
49147
165211
190
113416
151252
83149
106117
469
36916
131272
811411
101545
421
321316
151414
67129
101185
476
361312
101581
16927
541114
216
231316
151441
851110
91267
228
231514
131641
85912
111067
224
231415
131614
761110
12985
218
231415
713410
166111
91258
473
361213
16972
541411
101518
422
321316
151414
101185
67129
478
361312
16927
101581
541114
217
231316
151441
12976
581011
229
231514
131641
12958
761011
225
231415
131614
111076
85129
219
231415
716110
136114
12985
483
361510
131218
271411
16945
445
321613
151441
67912
101158
487
36169
101554
131227
811114
236
231613
151414
581110
12967
230
231514
161314
58129
111067
226
231415
161341
761110
91258
221
231415
111346
161071
58912
485
361510
16945
271411
131218
446
321613
151441
101158
67912
489
36169
131227
101554
811114
237
231613
151414
91276
851011
231
231514
161314
91285
761011
227
231415
161341
111076
58912
223
231415
111616
131074
85129
530
310516
138112
121147
61549
450
351016
121417
131182
64159
535
310138
165211
615121
94714
250
251116
151261
831310
91447
264
251512
111661
83914
131047
255
251215
111616
741310
14983
252
251215
711610
164131
91438
532
310813
165112
94147
615112
464
351610
121471
64915
131128
539
310165
138211
61594
121714
251
251116
151261
14974
381013
265
251512
111661
14938
741013
256
251215
111616
131074
83149
253
251215
716110
114136
14983
536
310156
138112
211147
16549
465
351610
121471
131128
64915
558
313612
16297
108151
511414
273
251611
151216
381310
14947
266
251512
161116
38149
131047
261
251215
161161
741310
91438
257
251215
131164
161071
38914
537
310156
16549
211147
138112
503
381013
91447
161152
611512
562
313108
162511
612151
97414
274
251611
151216
91474
831013
267
251512
161116
91483
741013
262
251215
161161
131074
38914
258
251215
131614
111076
83149
560
313810
162115
97144
612115
505
381310
91474
611215
161125
628
451411
91672
151018
631213
321
281113
15964
531610
121417
280
27916
121336
151081
541411
287
271114
91645
811312
151063
286
271114
813112
94165
151063
565
313126
16279
511144
108115
506
381310
91474
161125
611215
632
451411
151018
91672
631213
322
281113
15964
141271
351016
282
27916
141154
151081
361213
288
271114
121318
54169
151063
295
271312
811114
96163
151045
621
451015
141181
721312
91636
583
411415
161323
581110
91276
635
451510
91663
141118
721213
325
281311
15946
351610
141217
291
271213
91636
151054
811411
296
271312
91663
811114
151045
314
28915
161161
131074
351214
623
451114
151081
631312
91627
584
411415
161323
91276
581110
637
451510
141118
91663
721213
326
281311
15946
121471
531016
293
271213
141181
151054
36916
298
271312
141118
36169
151045
315
28915
161341
111076
531412
646
45169
141127
181312
151036
591
411514
161332
581011
91267
695
49147
156112
516112
103813
333
29716
158101
123136
514411
301
271411
91654
151036
811213
307
27169
121363
541114
151018
336
29815
117106
164131
514312
647
45169
151036
181312
141127
592
411514
161332
91267
581011
698
49156
147112
516103
112813
334
29716
158101
145114
312613
302
271411
121381
151036
54916
309
27169
141145
361312
151018
337
29815
111616
741310
145123
690
49615
147121
112138
516310
648
46915
111328
141271
531610
741
414511
151108
97162
612313
350
29167
158110
312136
145411
328
28159
111364
531214
161017
310
28915
111346
711610
141253
338
29815
137104
166111
312514
691
49714
156121
103138
516211
661
46159
111382
531016
141217
746
41497
151612
511162
108313
351
29167
158110
514114
123613
329
28159
111364
141235
711016
311
28915
111346
161071
531412
339
29815
131614
761110
123145
702
49165
147211
112138
156310
662
46159
111382
141217
531016
789
54169
101536
111427
811312
384
212713
155104
93166
814111
330
28159
131146
351412
161017
312
28915
131164
711610
121435
359
211714
121318
54169
156103
704
49165
156310
112138
147211
668
47914
101338
151261
521611
790
54169
111427
101536
811312
385
212713
155104
148111
39616
331
28159
131146
121453
711016
313
28915
131164
161071
351214
366
211138
127114
510163
15649
744
41479
151126
108133
511216
678
47149
101383
521116
151216
803
510118
163213
415141
96712
386
212137
155410
39166
148111
344
29158
167110
312145
136411
341
29815
167101
114136
514312
382
212515
167101
136114
39814
748
414115
151810
612133
97216
679
47149
101383
151216
521116
808
511108
162313
414151
97612
387
212137
155410
814111
93616
345
29158
167110
514123
114613
342
29815
167101
136114
312514
383
212515
161341
761110
93148
785
541411
16972
361213
101518
768
521611
151261
47914
101338
834
631510
91645
121318
721411
399
214711
153106
95164
812113
356
211516
14794
156121
310813
367
211138
147112
310165
15649
391
213712
141118
36169
154105
788
541510
16963
271213
111418
779
531610
141271
46915
111328
835
631510
121318
91645
721411
400
214711
153106
128131
59416
362
211813
147121
15694
310516
378
211165
14749
310138
156112
394
213118
147112
310165
15469
828
631312
151081
451114
91627
818
611512
161152
381013
91447
850
69127
154114
316132
105811
401
214117
153610
59164
128113
388
212155
137410
39148
166111
379
212515
137104
111166
81439
397
214315
167101
114136
59812
839
63169
151054
181114
121327
844
64159
131182
351016
121417
860
61297
151414
313162
108511
402
214117
153610
812131
95416
389
212155
137410
81493
111616
380
212515
137104
166111
39814
398
214315
161161
741310
95128
419
321316
141541
851011
91276
423
321415
131641
85912
101176
432
321514
131614
671011
12985
427
321514
613411
167101
91258
420
321316
141541
12967
581110
424
321415
131641
12958
671110
433
321514
131614
101167
85129
428
321514
616111
137104
12985
443
321613
141514
581011
12976
425
321415
161314
58129
101176
435
321514
161341
671011
91258
429
321514
101347
161161
58912
444
321613
141514
91267
851110
426
321415
161314
91285
671110
436
321514
161341
101167
58912
430
321514
101617
131164
85129
451
351016
141271
821311
91546
460
351412
101671
82915
131146
456
351214
101617
131164
82159
452
351214
610711
164131
91528
466
351610
141217
281311
15946
461
351412
101671
15928
641113
459
351214
161071
641311
91528
457
351214
131614
101167
82159
467
351610
141217
91564
821113
462
351412
161017
28159
131146
475
361312
91672
811015
141145
474
361312
810115
97162
141145
504
381013
14974
521611
121516
463
351412
161017
91582
641113
477
361312
151018
27169
141145
502
38914
161341
101167
521512
507
381310
14947
251611
151216
468
36916
121327
141181
541510
488
36169
121372
541015
141118
516
39814
106117
164131
515212
508
381310
14947
121561
521116
471
361213
91627
141154
811510
490
36169
151045
271312
141118
520
39814
131614
671011
122155
515
39616
148111
122137
515410
479
361510
91654
141127
811213
498
38914
101347
161161
521512
533
310138
126115
511162
14749
527
39166
148111
212137
155410
481
361510
121381
141127
54916
499
38914
131074
611611
121525
547
312514
161341
671011
92158
528
39166
148111
515104
122713
511
38149
101374
521215
161116
521
39814
166111
104137
515212
557
313612
151018
27169
144115
548
312613
145114
92167
815110
512
38149
101374
151225
611116
534
310138
156112
211165
14749
561
313108
156112
211165
14479
549
312136
145411
29167
158110
513
38149
131047
251512
161116
540
310165
15649
211138
147112
573
315214
166111
104137
59812
550
312136
145411
815101
92716
514
38149
131047
121552
611116
543
312514
136114
101167
81529
574
315214
161071
641311
95128
566
314512
15298
107161
611413
523
39148
166111
212155
137410
599
411613
141523
58912
111076
593
411613
514312
15892
101167
569
31489
152125
107134
611116
524
39148
166111
515122
104713
600
411613
141523
91258
761110
594
411613
515212
14893
111076
570
31498
152512
611161
107413
553
312145
136411
29158
167110
603
411613
151432
58912
101167
596
411613
91438
151252
671011
572
314125
15289
611134
107116
554
312145
136411
81592
101716
604
411613
151432
91258
671011
597
411613
91528
141253
761110
581
411415
131632
76912
101185
575
411316
141532
761011
91285
630
451411
101581
72916
131236
626
451411
79216
108151
131236
582
411415
131632
111058
67129
576
411316
141532
111067
58129
633
451411
16927
181510
131236
634
451510
69316
118141
131227
589
411514
131623
67912
111085
577
411316
151423
671110
91285
636
451510
111481
63916
131227
653
461113
141523
91258
711610
590
411514
131623
101158
76129
578
411316
151423
101176
58129
638
451510
16936
181411
131227
673
471013
151432
91258
611611
649
46915
131182
711412
101635
620
451015
111418
131272
63169
651
461113
91528
141253
711610
694
49147
115216
612151
138310
663
46159
131128
171412
161035
622
451114
101518
131263
72169
654
461113
15982
531412
101617
697
49156
105316
712141
138211
664
46159
131128
101653
711214
640
45169
101563
131218
721114
670
471013
91438
151252
611611
707
410713
141523
58912
111166
669
47914
131083
611512
111625
642
45169
111472
131218
631015
671
471013
14983
521512
111616
718
411613
151432
58912
101167
681
47149
131038
161512
161125
657
461311
91582
711016
141235
696
49147
165211
112156
138310
743
414511
16927
181510
133126
682
47149
131038
111652
611215
658
461311
91582
161017
531214
699
49156
165310
112147
138211
747
41497
165211
112156
133810
705
410515
137122
111148
61639
659
461311
15928
171610
141235
708
410713
155122
93148
616111
750
415510
16936
181411
132127
712
410155
137212
111148
16639
660
461311
15928
101671
531214
716
411613
145123
92158
716110
752
41596
165310
112147
132811
713
410155
137212
61693
111814
674
471310
91483
611116
151225
761
521512
111616
101347
83149
756
521512
411613
167101
91438
715
411514
136123
101158
71629
675
471310
91483
161116
521215
763
521512
161161
471013
91438
760
521512
101617
111346
83149
722
411145
136312
110158
16729
676
471310
14938
161611
151225
771
531412
101617
111346
82159
769
531412
410713
166111
91528
723
411145
136312
71692
101815
677
471310
14938
111661
521215
774
531412
161071
461113
91528
772
531412
111616
101347
82159
730
413611
161107
98152
512314
709
410137
155212
111166
14839
791
54169
141172
361015
121318
801
510118
144115
313162
12769
731
413710
161116
98143
512215
710
410137
155212
616111
93814
792
54169
151063
271114
121318
807
511108
154114
213163
12679
734
413107
161611
512152
98314
720
411136
145312
110167
15829
802
510118
154114
213163
12769
813
514312
161161
471013
92158
735
413116
161710
512143
98215
721
411136
145312
716101
92815
806
511108
144115
313162
12679
816
515212
161071
461113
93148
766
521611
121516
91447
831310
784
541411
91627
121336
811510
822
611611
121525
91438
741310
819
611611
312514
15892
101347
778
531610
121417
91546
821311
787
541510
91636
121327
811411
824
611611
151252
38914
101347
821
611611
91528
121435
741310
809
51298
143215
413161
116710
797
59128
164113
214153
117610
836
631510
131281
45916
111427
833
631510
49516
138121
111427
810
51298
152314
413161
107611
798
59128
164113
315142
106711
837
631510
16954
181213
111427
841
641311
121525
91438
711610
817
611512
111625
101338
74149
827
631312
101518
111445
72169
840
641311
91528
121435
711610
849
69127
133216
414151
118510
843
64159
111328
101635
711412
838
63169
101545
111418
721312
842
641311
15982
351214
101617
861
61297
163213
114154
115810
854
611107
134116
314152
12589
852
610117
153214
113164
12859
851
69127
163213
114154
118510
862
613411
151252
38914
101167
855
611107
161413
314152
98512
853
610117
153214
416131
95812
859
61297
133216
414151
115810
864
615310
16954
181213
112147

MAGIC SQUARES USING TWO CATCHUP BASE SQUARES

The order-4 magic squares that use two catchup base squares in order to have main diagonals that add correctly are shown in the table below. There are eight groups of squares that have this catchup property. Each group can be created from four different base square quartets. These four base square quartets generate the same group of Frénicle magic squares after rearrangement using Frénicle's rules. An example is given below. In the example the B8 and B7 base squares are not the same as the B4 and B3 given in the "Order-4 Magic Squares with Two Catchup Base Squares" table given below for 2Catchup Group 1, they are complements of predictable base squares, however, and therefore interchangeable

Interconversion of the Four Base Square Quartets of 2Catchup Group 1
The First Base Square Quartet of 2Catchup Group 1
A1
1010
0101
1010
0101
E17
1100
1010
0011
0101
B1
0101
1010
1010
0101
B4
0110
1001
0110
1001
First Base Square Quartet Transposed
A1
1010
0101
1010
0101
E18
1100
1001
0110
0011
B2
0110
1001
0110
1001
B3
0101
1010
1010
0101
First Base Square Quartet Rotated 180°
A1
1010
0101
1010
0101
E21
1010
1100
0101
0011
B1
0101
1010
1010
0101
B8
1001
0110
1001
0110
First Base Square Quartet Transposed and Rotated 180°
A1
1010
0101
1010
0101
E22
1100
0110
1001
0011
B2
0110
1001
0110
1001
B7
1010
0101
0101
1010

The four base square quartets are shown at the top of each group. The two base squares within the parentheses are the catchup squares. The other two base squares have predictable main diagonals. There are 24 Frénicle squares in each group of this section. The properties of the squares within each group are the same except for groups five and six which each have four squares with an additional broken diagonal feature. A more detailed description of the features of each group is given in ORDER-4 MAGIC SQUARES USING TWO CATCHUP BASE SQUARES.

Some of the numbers within the magic squares are in blue. These are the top numbers of a diamond shaped features that adds to 34. All of the diamond shaped features require catchup. Pairs of groups have similar patterns of diamond shaped figures.

Order-4 Magic Squares with Two Catchup Base Squares
2Catchup Group 1
(A1+E17)+B1+B4
(A1+E18)+B2+B3
(A1+E21)+B1+B4
(A1+E22)+B2+B3

24 squares
part.pan diagonal
Walkington T4.03.2
Dudeney Group VII
2x2 sub-square pattern
3434
3434
3434
3434
2Catchup Group 2
(A1+E7)+B1+B4
(A1+E8)+B2+B3
(A1+E19)+B1+B4
(A1+E20)+B2+B3

24 squares
part.pan diagonal
Walkington T4.03.2
Dudeney Group IX
2x2 sub-square pattern
3434
3434
3434
3434
2Catchup Group 3
(C3+F7)+B2+C2
(C3+F8)+B1+C1
(C3+F27)+B2+C2
(C3+F28)+B1+C1

24 squares
simple
Walkington T4.05.4
Dudeney Group VIII
2x2 sub-square pattern
3434
3434
2Catchup Group 4
(C3+F21)+B2+C2
(C3+F22)+B1+C1
(C3+F25)+B2+C2
(C3+F26)+B1+C1

24 squares
simple
Walkington T4.05.4
Dudeney Group X
2x2 sub-square pattern
3434
3434
2Catchup Group 5
(F3+E8)+C1+F1
(F3+E20)+C1+F1
(F4+E7)+C2+F1
(F4+E19)+C2+F1
20 simple squares
Walkington T4.05.4
4 part.pan diagonal
Walkington T4.04
Dudeney Group VIII
2x2 sub-square pattern
3434
3434
2Catchup Group 6
(F3+E17)+C2+F2
(F3+E21)+C2+F2
(F4+E18)+C1+F2
(F4+E22)+C1+F2
20 simple squares
Walkington T4.05.4
4 part.pan diagonal
Walkington T4.04
Dudeney Group X
2x2 sub-square pattern
3434
3434
2Catchup Group 7
(F3+F22)+B3+F1
(F3+F26)+B3+F1
(F4+F21)+B4+F1
(F4+F25)+B4+F1

24 squares
simple
Walkington T4.05.2
Dudeney Group VII
2x2 sub-square pattern
3434
3434
3434
3434
2Catchup Group 8
(F3+F7)+B4+F2
(F3+F27)+B4+F2
(F4+F8)+B3+F2
(F4+F28)+B3+F2

24 squares
simple
Walkington T4.05.2
Dudeney Group IX
2x2 sub-square pattern
3434
3434
3434
3434
271
251611
131218
47149
151036
105
181015
161332
541411
12976
10
131614
131524
86119
121057
238
241315
141631
751012
11986
8
131614
81529
136114
121057
260
251215
141631
11968
741310
268
251611
812113
97144
151036
23
141415
161152
96127
813310
303
271411
131038
45169
151216
118
181312
161125
361510
14947
11
131614
131524
121075
86911
239
241315
141631
11968
751210
9
131614
121525
131074
86911
263
251215
161413
91186
741310
300
271411
810313
95164
151216
29
141514
161053
97126
813211
347
29167
138112
411145
156310
180
112138
16729
310156
145411
20
141415
91267
165112
813310
240
241315
161413
571210
11986
40
151612
81439
104137
151126
340
29815
141631
751012
114136
346
29167
128113
511144
156310
142
110815
161332
541411
12796
371
211147
136312
49165
158110
200
114415
161152
96127
831310
26
141514
91276
165103
813211
241
241315
161413
91186
751210
43
151612
151432
101167
84913
343
29815
161413
571210
114136
369
211147
126313
59164
158110
145
110158
16639
511144
127213
439
321613
101518
76129
141154
207
115414
161053
97126
821311
41
151612
101437
84139
151126
413
311614
131542
86911
101257
128
19168
141253
461113
157210
431
321514
121651
13948
671011
438
321613
815110
96127
141154
193
113812
161125
361510
14497
472
361213
101158
72169
141514
208
115108
16639
511144
122713
42
151612
101437
151162
84913
414
311614
131542
121057
68911
129
19168
151252
471013
146311
434
321514
161215
91384
671011
453
351214
61189
152134
101617
197
113128
16729
310156
144511
486
361510
161125
181312
14947
272
251611
151036
47149
131218
212
231316
101158
156121
71449
415
311614
151324
68119
101257
242
241513
514312
167101
11968
500
38914
131542
121057
611611
455
351214
89611
134152
101617
215
231316
151261
105118
71449
510
381310
16945
161512
141127
283
27916
151441
631312
111085
232
231613
101185
15694
714112
416
311614
151324
101275
68911
243
241513
91438
161161
751012
501
38914
151324
101275
611611
470
361213
811510
92167
141514
235
231613
15964
108115
714112
525
39166
108115
713122
144511
349
29167
156310
411145
138112
244
241513
161431
571012
11968
491
371014
121651
621115
13984
275
261511
713410
93148
161215
519
39814
121651
621115
137104
517
39814
107125
152134
616111
335
29716
151441
631312
118105
531
310714
13498
125161
615211
390
213316
151261
105118
74149
245
241513
161431
91168
751012
492
371014
121651
13948
621511
278
261511
161341
91258
731014
522
39814
161215
261511
137104
518
39814
125107
134152
616111
348
29167
155410
612133
118114
538
310156
16729
112138
145411
407
215611
165121
94138
710314
276
261511
91348
731410
161215
493
371014
161215
261511
13984
353
210157
131164
351214
16819
544
312514
131542
86911
101167
529
39166
158110
213127
144511
405
215413
166111
93148
710512
552
312136
16549
110158
147211
408
215107
16981
361114
134512
277
261511
91348
161251
731014
494
371014
161215
91384
621511
354
210157
161161
38914
135412
546
312514
151324
68119
101167
564
313126
154510
29167
148111
406
215413
161071
531412
11698
692
49813
107143
152116
516112
442
321613
141154
76129
101518
411
311416
131524
86119
101275
684
48913
111562
141037
511612
409
311416
81529
136114
101275
598
411613
111562
141037
58912
714
410155
16729
114118
133612
418
321316
141271
115108
61549
693
49813
143107
116152
516112
509
381310
141127
161512
16945
412
311416
131524
121075
68119
685
48913
151126
101473
511612
410
311416
121525
131074
68119
601
411613
151126
101473
58912
749
414115
16369
110158
137212
441
321613
14974
118105
615112
765
521611
415114
131083
12796
526
39166
144511
713122
108115
417
321316
111058
147121
61549
753
511612
101473
84913
111526
437
321613
71269
145114
101518
759
521512
81691
113614
101347
757
521512
41389
143107
111616
559
313810
141127
161512
16495
775
531610
414115
131182
12697
551
312136
147211
110158
16549
440
321613
111085
14794
615112
754
511612
141037
48139
111526
495
371410
91258
161341
621115
762
521512
16819
311146
101347
758
521512
89413
107143
111616
563
313126
147211
110158
16459
782
541312
107215
89161
111436
555
313216
141271
115108
64159
496
371410
161251
261115
13948
794
581011
131623
49714
121156
541
311146
131074
251215
16819
770
531412
81691
102715
111346
767
521611
141514
310813
12796
567
314710
164131
95128
611215
783
541312
116314
89161
101527
571
314116
16981
271015
134512
497
371410
161251
91348
621115
796
581110
131632
49615
121147
542
311146
161071
28915
135412
773
531412
16819
210157
111346
781
531610
151414
211813
12697
568
314710
161161
251215
13498
786
541411
161332
181015
12976
588
411514
131263
851110
91627
579
411415
12967
138112
516310
811
513412
16819
210157
113146
585
411514
811510
136123
91627
800
510811
151441
27916
123136
799
510811
14794
321613
121516
580
411415
131182
12697
516310
795
581011
16972
141415
121336
644
45169
131038
271411
151216
586
411514
12976
138103
516211
812
513412
16819
311146
102157
605
421315
514312
167101
91186
814
514411
151081
231316
12796
805
511810
15694
231613
121417
587
411514
131083
12796
516211
829
631411
413125
152710
91618
701
49165
136312
211147
158110
607
421315
161431
571012
91186
847
67129
141541
310516
112138
606
421315
91438
161161
571210
820
611611
715102
124513
91438
845
64159
161323
112714
115108
728
413215
166111
93148
512710
831
631411
125413
710152
91618
711
410155
133612
814111
97216
608
421315
161431
91168
571210
863
614311
157210
412135
91168
686
48139
101167
151432
511216
823
611611
157210
412135
91438
858
61279
165103
141514
111328
729
413215
161071
531412
98116
867
721510
413125
143611
91618
736
413125
141163
18916
152710
687
48139
151162
151216
141037
876
76129
151441
211516
103138
726
412135
14983
161116
157210
865
711610
614113
124513
91528
873
74149
161332
112615
105118
732
41389
153142
106117
512116
868
721510
125413
611143
91618
737
413125
151072
18916
143611
688
48139
151162
101437
511216
880
71449
156121
231316
101158
727
412135
15982
171016
146311
866
711610
146311
412135
91528
879
71269
165112
141415
101338
733
41389
151252
161116
143107

MAGIC SQUARES USING THREE CATCHUP BASE SQUARES

The order-4 magic squares that use three catchup base squares in order to have main diagonals that add correctly are shown in the table below. There are 28 groups of squares that have this catchup property. Each group can be created from four different base square quartets. These four base square quartets generate the same group of Frénicle magic squares because they represent different orientations of the four base squares.

This table is split into four sub sections with 8 groups in each of the first three sub sections and 4 groups in the last sub section. Four base square quartets are shown at the top of each group. The three base squares within the parentheses are the catchup squares. The other base square is predictable. There are 4 squares in each group of this section. The properties of the group members within each group are the same. A more detailed description of the features of each group is given in ORDER-4 MAGIC SQUARES USING THREE CATCHUP BASE SQUARES.

Order-4 Magic Squares with Three Catchup Base Squares
3Catchup Group 1
(A1+E1+E19)+B1
(A1+E2+E20)+B2
(A1+E5+E7)+B1
(A1+E6+E8)+B2
4 part.pan diagonal
Walkington T4.03.1
Dudeney Group VI
2x2 sub-square pattern
3434
3434
3434
3434
3Catchup Group 2
(A1+E3+E17)+B1
(A1+E4+E18)+B2
(A1+E23+E21)+B1
(A1+E24+E22)+B2
4 part.pan diagonal
Walkington T4.03.1
Dudeney Group VI
2x2 sub-square pattern
3434
3434
3434
3434
3Catchup Group 3
(A1+E1+E19)+B4
(A1+E2+E20)+B3
(A1+E5+E7)+B4
(A1+E6+E8)+B3
4 part.pan diagonal
Walkington T4.03.3
Dudeney Group XI
2x2 sub-square pattern
3434
3434
3434
3434
3Catchup Group 4
(A1+E3+E17)+B4
(A1+E4+E18)+B3
(A1+E23+E21)+B4
(A1+E24+E22)+B3
4 part.pan diagonal
Walkington T4.03.3
Dudeney Group XI
2x2 sub-square pattern
3434
3434
3434
3434
3Catchup Group 5
(A1+E1+E7)+B1
(A1+E2+E8)+B2
(A1+E5+E19)+B1
(A1+E6+E20)+B2
4 simple
Walkington T4.05.1
Dudeney Group VI
2x2 sub-square pattern
3434
3434
3434
3434
3Catchup Group 6
(A1+E3+E21)+B1
(A1+E4+E22)+B2
(A1+E23+E17)+B1
(A1+E24+E18)+B2
4 simple
Walkington T4.05.1
Dudeney Group VI
2x2 sub-square pattern
3434
3434
3434
3434
3Catchup Group 7
(A1+E1+E21)+B4
(A1+E2+E22)+B3
(A1+E5+E17)+B4
(A1+E6+E18)+B3
4 simple
Walkington T4.05.2
Dudeney Group VII
2x2 sub-square pattern
3434
3434
3434
3434
3Catchup Group 8
(A1+E3+E7)+B4
(A1+E4+E8)+B3
(A1+E23+E19)+B4
(A1+E24+E20)+B3
4 simple
Walkington T4.05.2
Dudeney Group IX
2x2 sub-square pattern
3434
3434
3434
3434
100
18916
141343
721510
121165
285
271015
111256
81169
131434
181
112138
16945
271411
156310
364
211813
15496
105163
714112
52
161116
141523
741310
12985
222
231415
111616
85129
131074
700
49165
118114
615103
132712
172
112615
16972
138103
451114
179
112138
151036
271411
16549
482
361510
138112
49165
141127
202
114712
165103
94156
811213
484
361510
147211
49165
131218
152
111616
121435
137104
82159
454
351214
616111
15982
104137
717
411613
15298
107161
514312
205
114118
16549
712132
103615
376
211147
16945
181312
156310
645
45169
147211
310156
131218
374
211147
151036
181312
16549
643
45169
138112
310156
141127
370
211147
121381
54916
156310
639
45169
615103
112714
131218
869
72169
615112
111445
103138
358
211516
151081
14794
361213
617
431413
151072
651211
91618
793
561112
16981
341314
101527
724
411145
152710
613123
98116
689
49615
118132
141127
516310
602
411613
151252
671011
91438
764
521512
161341
38914
101167
875
761110
143215
413161
91258
373
211147
154510
813121
96316
3Catchup Group 9
(C3+F5+F7)+B2
(C3+F6+F8)+B1
(C3+F9+F27)+B2
(C3+F10+F28)+B1
4 simple
Walkington T4.05.1
Dudeney Group VI
2x2 sub-square pattern
3434
3434
3434
3434
3Catchup Group 10
(C3+F11+F25)+B2
(C3+F12+F26)+B1
(C3+F23+F21)+B2
(C3+F24+F22)+B1
4 simple
Walkington T4.05.1
Dudeney Group VI
2x2 sub-square pattern
3434
3434
3434
3434
3Catchup Group 11
(C3+F5+F27)+B2
(C3+F6+F28)+B1
(C3+F9+F7)+B2
(C3+F10+F8)+B1
4 part.pan diagonal
Walkington T4.03.1
Dudeney Group VI
2x2 sub-square pattern
3434
3434
3434
3434
3Catchup Group 12
(C3+F11+F21)+B2
(C3+F12+F22)+B1
(C3+F23+F25)+B2
(C3+F24+F26)+B1
4 part.pan diagonal
Walkington T4.03.1
Dudeney Group VI
2x2 sub-square pattern
3434
3434
3434
3434
3Catchup Group 13
(C3+F5+F7)+C2
(C3+F6+F8)+C1
(C3+F9+F27)+C2
(C3+F10+F28)+C1
4 simple
Walkington T4.05.3
Dudeney Group XII
2x2 sub-square pattern
3434
3434
3Catchup Group 14
(C3+F11+F25)+C2
(C3+F12+F26)+C1
(C3+F23+F21)+C2
(C3+F24+F22)+C1
4 simple
Walkington T4.05.3
Dudeney Group XII
2x2 sub-square pattern
3434
3434
3Catchup Group 15
(C3+F5+F25)+C2
(C3+F6+F26)+C1
(C3+F9+F21)+C2
(C3+F10+F22)+C1
4 simple
Walkington T4.05.4
Dudeney Group X
2x2 sub-square pattern
3434
3434
3Catchup Group 16
(C3+F11+F7)+C2
(C3+F12+F8)+C1
(C3+F23+F27)+C2
(C3+F24+F28)+C1
4 simple
Walkington T4.05.4
Dudeney Group VIII
2x2 sub-square pattern
3434
3434
2
121516
131434
127105
81169
318
281113
101653
711214
15964
50
161116
131074
123145
81529
320
281113
141217
351610
15964
3
121615
131443
12796
811510
319
281113
101653
15946
711412
652
461113
101671
15928
531412
58
161215
131083
16792
411514
87
171412
91546
821311
161035
448
341314
151612
69811
105127
91
171412
111328
64159
161035
545
312514
15892
611611
101347
88
171412
91546
161053
821113
449
341413
151621
69712
105118
655
461113
161017
91582
531412
94
171610
111346
141253
82915
211
211615
141343
11896
712510
619
431413
161521
510712
96118
259
251215
14983
114136
716110
719
411613
167101
521512
91438
209
211516
141334
118105
71269
613
431314
161512
510811
96127
872
74149
111625
613312
101158
248
251116
14974
158101
312613
665
46159
141271
351016
131128
777
531610
111382
64915
121417
667
46159
161053
171214
131128
780
531610
15946
281311
121417
666
46159
141271
111328
531016
650
46915
141217
111382
531610
877
711610
164113
214153
95128
332
28159
141253
111346
711016
3Catchup Group 17
(F3+E1+F7)+F2
(F3+E5+F27)+F2
(F4+E2+F8)+F2
(F4+E6+F28)+F2
4 simple
Walkington T4.05.1
Dudeney Group VI
2x2 sub-square pattern
3434
3434
3434
3434
3Catchup Group 18
(F3+E4+F26)+F1
(F3+E24+F22)+F1
(F4+E3+F25)+F1
(F4+E23+F21)+F1
4 simple
Walkington T4.05.1
Dudeney Group VI
2x2 sub-square pattern
3434
3434
3434
3434
3Catchup Group 19
(F3+E1+F27)+F2
(F3+E5+F7)+F2
(F4+E2+F28)+F2
(F4+E6+F8)+F2
4 simple
Walkington T4.05.1
Dudeney Group VI
2x2 sub-square pattern
3434
3434
3434
3434
3Catchup Group 20
(F3+E4+F22)+F1
(F3+E24+F26)+F1
(F4+E3+F21)+F1
(F4+E23+F25)+F1
4 simple
Walkington T4.05.1
Dudeney Group VI
2x2 sub-square pattern
3434
3434
3434
3434
3Catchup Group 21
(F3+F6+E8)+F1
(F3+F10+E20)+F1
(F4+F5+E7)+F1
(F4+F9+E19)+F1
4 simple
Walkington T4.05.1
Dudeney Group VI
2x2 sub-square pattern
3434
3434
3434
3434
3Catchup Group 22
(F3+F11+E21)+F2
(F3+F23+E17)+F2
(F4+F12+E22)+F2
(F4+F24+E18)+F2
4 simple
Walkington T4.05.1
Dudeney Group VI
2x2 sub-square pattern
3434
3434
3434
3434
3Catchup Group 23
(F3+F6+E20)+F1
(F3+F10+E8)+F1
(F4+F5+E19)+F1
(F4+F9+E7)+F1
4 simple
Walkington T4.05.1
Dudeney Group VI
2x2 sub-square pattern
3434
3434
3434
3434
3Catchup Group 24
(F3+F11+E17)+F2
(F3+F23+E21)+F2
(F4+F12+E18)+F2
(F4+F24+E22)+F2
4 simple
Walkington T4.05.1
Dudeney Group VI
2x2 sub-square pattern
3434
3434
3434
3434
1
121516
121435
137104
81169
220
231415
81619
115126
131074
47
161116
121075
133144
81529
284
271015
81259
111166
131434
44
161116
715210
144133
12985
352
210715
111616
85129
133144
86
171412
813211
94156
161035
363
211813
141217
351610
15694
127
19816
141523
741310
126115
458
351214
151612
69811
104137
156
111616
141343
721510
12895
556
313414
15892
611611
101257
153
111616
131434
127105
82159
447
341314
616111
15982
105127
194
113128
151036
271411
16459
480
361510
128113
59164
141127
210
211615
111346
14893
712510
656
461113
161521
510712
93148
254
251215
11986
144133
716110
740
414313
167101
521512
91168
381
212515
141343
11896
711610
614
431413
515212
161071
96118
404
214117
16945
181312
153610
641
45169
117214
610153
131218
739
414313
151252
671011
91168
755
521512
313414
16891
101167
751
41569
161053
171214
132118
776
531610
69415
118132
121417
595
411613
612511
157102
91438
804
511612
161341
38914
102157
615
431413
610711
155122
91618
815
515212
16981
341314
106117
3Catchup Group 25
(F3+E1+E21)+C2
(F3+E5+E17)+C2
(F4+E2+E22)+C1
(F4+E6+E18)+C1
4 simple
Walkington T4.05.4
Dudeney Group X
2x2 sub-square pattern
3434
3434
3Catchup Group 26
(F3+E4+E8)+C1
(F3+E24+E20)+C1
(F4+E3+E7)+C2
(F4+E23+E19)+C2
4 simple
Walkington T4.05.4
Dudeney Group VIII
2x2 sub-square pattern
3434
3434
3Catchup Group 27
(F3+F6+F26)+B3
(F3+F10+F22)+B3
(F4+F5+F25)+B4
(F4+F9+F21)+B4
4 simple
Walkington T4.05.2
Dudeney Group VII
2x2 sub-square pattern
3434
3434
3434
3434
3Catchup Group 28
(F3+F11+F7)+B4
(F3+F23+F27)+B4
(F4+F12+F8)+B3
(F4+F24+F28)+B3
4 simple
Walkington T4.05.2
Dudeney Group IX
2x2 sub-square pattern
3434
3434
3434
3434
616
431413
101671
15928
561112
99
171610
141343
111256
82915
703
49165
148111
315106
132712
59
161215
16972
138103
411514
618
431413
161017
91582
561112
170
112615
131083
16792
451114
738
414313
15298
107161
511612
161
111148
16549
712132
106315
871
74149
516211
121336
101158
327
28159
111256
141343
711016
870
72169
121516
514411
103138
249
251116
151081
14794
312613
874
751210
164113
214153
91168
357
211516
14974
158101
361213
878
712510
143215
413161
96118
403
214117
154510
813121
93616

MAGIC SQUARES USING FOUR CATCHUP BASE SQUARES

The order-4 magic squares that require four catchup base squares in order to have main diagonals that add correctly are shown in the table below. There are 24 groups of squares that have this catchup property. Each group can be created from four different base square quartets. These four base square quartets generate the same group of Frénicle magic squares because they represent different orientations of the same base squares.

The four base square quartets are shown at the top of each group. In this table there are three sub sections of eight groups each. All four base squares are in the parentheses because they are all catchup squares. The two middle base squares are in brackets because their multipliers can be exchanged. There are only 2 squares in each group of this section. The properties of the group members within each group are the same. A more detailed description of the features of each group is given in ORDER-4 MAGIC SQUARES USING FOUR CATCHUP BASE SQUARES.

Order-4 Magic Squares with Four Catchup Base Squares
4Catchup Group 1
(A1+[E1+E3]+E7)
(A1+[E2+E4]+E8)
(A1+[E5+E23]+E19)
(A1+[E6+E24]+E20)
2 simple
Walkington T4.05.1
Dudeney Group VI
2x2 sub-square pattern
3434
3434
3434
3434
4Catchup Group 2
(A1+[E1+E3]+E21)
(A1+[E2+E4]+E22)
(A1+[E5+E23]+E17)
(A1+[E6+E24]+E18)
2 simple
Walkington T4.05.1
Dudeney Group VI
2x2 sub-square pattern
3434
3434
3434
3434
4Catchup Group 3
(A1+[E1+E23]+E19)
(A1+[E2+E24]+E20)
(A1+[E3+E5]+E7)
(A1+[E4+E6]+E8)
2 simple
Walkington T4.05.1
Dudeney Group VI
2x2 sub-square pattern
3434
3434
3434
3434
4Catchup Group 4
(A1+[E1+E23]+E21)
(A1+[E2+E24]+E22)
(A1+[E3+E5]+E17)
(A1+[E4+E6]+E18)
2 simple
Walkington T4.05.1
Dudeney Group VI
2x2 sub-square pattern
3434
3434
3434
3434
4Catchup Group 5
(A1+[E1+E5]+E7)
(A1+[E1+E5]+E19)
(A1+[E2+E6]+E8)
(A1+[E2+E6]+E20)
2 simple
Walkington T4.05.1
Dudeney Group VI
2x2 sub-square pattern
3434
3434
3434
3434
4Catchup Group 6
(A1+[E3+E23]+E17)
(A1+[E3+E23]+E21)
(A1+[E4+E24]+E18)
(A1+[E4+E24]+E22)
2 simple
Walkington T4.05.1
Dudeney Group VI
2x2 sub-square pattern
3434
3434
3434
3434
4Catchup Group 7
(F3+[E1+E5]+F7)
(F3+[E1+E5]+F27)
(F4+[E2+E6]+F8)
(F4+[E2+E6]+F28)
2 simple
Walkington T4.05.1
Dudeney Group VI
2x2 sub-square pattern
3434
3434
3434
3434
4Catchup Group 8
(F3+[E4+E24]+F22)
(F3+[E4+E24]+F26)
(F4+[E3+E23]+F21)
(F4+[E3+E23]+F25)
2 simple
Walkington T4.05.1
Dudeney Group VI
2x2 sub-square pattern
3434
3434
3434
3434
131
110716
121345
15892
631411
624
451213
716110
141163
92158
166
112516
14983
156112
471013
683
47149
156112
211165
131038
143
110158
121363
541114
16729
627
451411
71692
101815
131236
4
131416
101347
156112
81259
672
471013
141613
59812
112156
134
110716
141163
15892
451213
830
631411
716110
121345
92158
186
112156
14947
381310
165211
848
67129
154114
213163
111058
144
110158
141145
361312
16729
631
451411
158110
29167
131236
36
151216
101167
154132
81439
742
414511
158110
29167
133126
4Catchup Group 9
(C3+[F5+F11]+F7)
(C3+[F6+F12]+F8)
(C3+[F9+F23]+F27)
(C3+[F10+F24]+F28)
2 simple
Walkington T4.05.1
Dudeney Group VI
2x2 sub-square pattern
3434
3434
3434
3434
4Catchup Group 10
(C3+[F5+F11]+F25)
(C3+[F6+F12]+F26)
(C3+[F9+F23]+F21)
(C3+[F10+F24]+F22)
2 simple
Walkington T4.05.1
Dudeney Group VI
2x2 sub-square pattern
3434
3434
3434
3434
4Catchup Group 11
(C3+[F5+F23]+F25)
(C3+[F6+F24]+F26)
(C3+[F9+F11]+F21)
(C3+[F10+F12]+F22)
2 simple
Walkington T4.05.1
Dudeney Group VI
2x2 sub-square pattern
3434
3434
3434
3434
4Catchup Group 12
(C3+[F5+F23]+F27)
(C3+[F6+F24]+F28)
(C3+[F9+F11]+F7)
(C3+[F10+F12]+F8)
2 simple
Walkington T4.05.1
Dudeney Group VI
2x2 sub-square pattern
3434
3434
3434
3434
4Catchup Group 13
(C3+[F5+F9]+F7)
(C3+[F5+F9]+F27)
(C3+[F6+F10]+F8)
(C3+[F6+F10]+F28)
2 simple
Walkington T4.05.1
Dudeney Group VI
2x2 sub-square pattern
3434
3434
3434
3434
4Catchup Group 14
(C3+[F11+F23]+F21)
(C3+[F11+F23]+F25)
(C3+[F12+F24]+F22)
(C3+[F12+F24]+F26)
2 simple
Walkington T4.05.1
Dudeney Group VI
2x2 sub-square pattern
3434
3434
3434
3434
4Catchup Group 15
(F3+[F6+F10]+E8)
(F3+[F6+F10]+E20)
(F4+[F5+F9]+E7)
(F4+[F5+F9]+E19)
2 simple
Walkington T4.05.1
Dudeney Group VI
2x2 sub-square pattern
3434
3434
3434
3434
4Catchup Group 16
(F3+[F11+F23]+E17)
(F3+[F11+F23]+E21)
(F4+[F12+F24]+E18)
(F4+[F12+F24]+E22)
2 simple
Walkington T4.05.1
Dudeney Group VI
2x2 sub-square pattern
3434
3434
3434
3434
7
131416
151342
12895
610711
612
421513
141613
711610
95128
725
412513
146113
711610
91528
78
171016
15982
124135
614311
6
131416
151342
106117
81259
611
421513
141613
59812
117106
168
112516
151342
106117
83149
609
421513
516112
14983
117106
39
151216
151162
14893
410713
826
621511
121615
713410
93148
856
61279
144115
313162
115108
79
171016
15982
146113
412513
38
151216
151162
104137
81439
706
410713
14893
511612
111526
199
114316
151162
104137
85129
629
451411
108115
79162
131236
4Catchup Group 17
(F3+[E1+F11]+E21)
(F3+[E5+F23]+E17)
(F4+[E2+F12]+E22)
(F4+[E6+F24]+E18)
2 simple
Walkington T4.05.1
Dudeney Group VI
2x2 sub-square pattern
3434
3434
3434
3434
4Catchup Group 18
(F3+[E4+F6]+E8)
(F3+[E24+F10]+E20)
(F4+[E3+F5]+E7)
(F4+[E23+F9]+E19)
2 simple
Walkington T4.05.1
Dudeney Group VI
2x2 sub-square pattern
3434
3434
3434
3434
4Catchup Group 19
(F3+[E1+F23]+E21)
(F3+[E5+F11]+E17)
(F4+[E2+F24]+E22)
(F4+[E6+F12]+E18)
2 simple
Walkington T4.05.1
Dudeney Group VI
2x2 sub-square pattern
3434
3434
3434
3434
4Catchup Group 20
(F3+[E4+F10]+E8)
(F3+[E24+F6]+E20)
(F4+[E3+F9]+E7)
(F4+[E23+F5]+E19)
2 simple
Walkington T4.05.1
Dudeney Group VI
2x2 sub-square pattern
3434
3434
3434
3434
4Catchup Group 21
(F3+[E1+F11]+F7)
(F3+[E5+F23]+F27)
(F4+[E2+F12]+F8)
(F4+[E6+F24]+F28)
2 simple
Walkington T4.05.1
Dudeney Group VI
2x2 sub-square pattern
3434
3434
3434
3434
4Catchup Group 22
(F3+[E4+F6]+F26)
(F3+[E24+F10]+F22)
(F4+[E3+F5]+F25)
(F4+[E23+F9]+F21)
2 simple
Walkington T4.05.1
Dudeney Group VI
2x2 sub-square pattern
3434
3434
3434
3434
4Catchup Group 23
(F3+[E1+F23]+F27)
(F3+[E5+F11]+F7)
(F4+[E2+F24]+F28)
(F4+[E6+F12]+F8)
2 simple
Walkington T4.05.1
Dudeney Group VI
2x2 sub-square pattern
3434
3434
3434
3434
4Catchup Group 24
(F3+[E4+F10]+F22)
(F3+[E24+F6]+F26)
(F4+[E3+F9]+F21)
(F4+[E23+F5]+F25)
2 simple
Walkington T4.05.1
Dudeney Group VI
2x2 sub-square pattern
3434
3434
3434
3434
610
421513
716110
141163
95128
138
110716
151162
14893
451213
680
47149
126115
511162
131038
167
112516
15982
146113
471013
5
131416
121345
15892
610711
625
451213
141613
711610
92158
72
171016
12985
154132
614311
745
41479
156112
211165
133108
825
621511
716110
121345
93148
139
110716
151342
12895
631411
846
67129
144115
313162
111058
198
114316
15982
124135
671011
37
151216
141163
15892
410713
832
631411
121615
713410
92158
75
171016
14983
156112
412513
857
61279
154114
213163
115108