4x4 Magic Square Solver: All Solutions

On Sunday, August 13th, 2006 I ran my 4x4 magic square script to completion for the set of all solutions. The results are recorded below.

This page lists all 924 possible solutions for a 4x4 magic square with the digits 1-16, i.e. where each row, column and diagonal has a sum of 34. If you find any discrepancies, duplications, or omissions, please let me know by leaving a comment on Transient Savant. As yet, I'm convinced that this is a comprehensive list.

To find the set of solutions for a specific puzzle, try using the magic square solver script itself.

Before: 1155527094.8817 seconds since the epoch

Solution #1

121516
131434
127105
81169

Solution #2

121516
121435
137104
81169

Solution #3

131416
151342
12895
610711

Solution #4

131416
151342
106117
81259

Solution #5

131416
121345
15892
610711

Solution #6

131416
101347
156112
81259

Solution #7

141316
151432
12985
671011

Solution #8

141316
151432
85129
101167

Solution #9

141316
141523
12985
761110

Solution #10

141316
141523
85129
111076

Solution #11

141316
121435
15982
671011

Solution #12

141316
121525
14983
761110

Solution #13

141316
81439
155122
101167

Solution #14

141316
81529
145123
111076

Solution #15

181015
141154
72169
121336

Solution #16

181015
121336
72169
141154

Solution #17

181114
151054
63169
121327

Solution #18

181114
121327
63169
151054

Solution #19

181312
151036
45169
141127

Solution #20

181312
141127
45169
151036

Solution #21

112615
14794
112165
813310

Solution #22

112615
813310
112165
14794

Solution #23

112714
15694
103165
813211

Solution #24

112714
813211
103165
15694

Solution #25

112138
156310
49165
147211

Solution #26

112138
147211
49165
156310

Solution #27

114415
12796
132163
811510

Solution #28

114415
811510
132163
12796

Solution #29

114712
15496
105163
811213

Solution #30

114712
811213
105163
15496

Solution #31

114118
154510
69163
127213

Solution #32

114118
127213
69163
154510

Solution #33

115414
12697
133162
810511

Solution #34

115414
810511
133162
12697

Solution #35

115612
14497
115162
810313

Solution #36

115612
810313
115162
14497

Solution #37

115108
144511
79162
126313

Solution #38

115108
126313
79162
144511

Solution #39

211516
141334
118105
71269

Solution #40

231316
151441
12976
581011

Solution #41

231316
151261
105118
71449

Solution #42

231316
151441
851110
91267

Solution #43

231316
141514
111085
76129

Solution #44

231316
141514
76129
111085

Solution #45

231316
101158
156121
71449

Solution #46

311416
131524
121075
68119

Solution #47

311416
131524
86119
101275

Solution #48

311416
121525
131074
68119

Solution #49

311416
81529
136114
101275

Solution #50

321316
141541
12967
581110

Solution #51

321316
141271
115108
61549

Solution #52

321316
141541
851011
91276

Solution #53

321316
151414
101185
67129

Solution #54

321316
151414
67129
101185

Solution #55

321316
111058
147121
61549

Solution #56

411316
141532
111067
58129

Solution #57

411316
141532
761011
91285

Solution #58

411316
151423
101176
58129

Solution #59

411316
151423
671110
91285

Solution #60

451411
151018
91672
631213

Solution #61

451510
141118
91663
721213

Solution #62

461311
15928
101671
531214

Solution #63

46159
131128
101653
711214

Solution #64

471310
14938
111661
521215

Solution #65

47149
131038
111652
611215

Solution #66

49147
156112
516112
103813

Solution #67

49156
147112
516103
112813

Solution #68

410137
155212
616111
93814

Solution #69

410155
137212
61693
111814

Solution #70

411136
145312
716101
92815

Solution #71

411145
136312
71692
101815

Solution #72

511216
151432
101167
48139

Solution #73

511216
101437
151162
48139

Solution #74

511216
101437
84139
111562

Solution #75

511216
81439
104137
111562

Solution #76

531412
15928
101671
461113

Solution #77

561112
15928
101671
431413

Solution #78

510154
147211
31696
121813

Solution #79

510154
117214
61693
121813

Solution #80

611116
121552
131047
38149

Solution #81

611116
121552
741013
91483

Solution #82

611116
151225
101374
38149

Solution #83

611116
151225
471310
91483

Solution #84

621511
13948
121651
371014

Solution #85

631213
151018
91672
451411

Solution #86

631510
121318
91645
721411

Solution #87

641113
15928
101671
351412

Solution #88

64159
111328
101635
711412

Solution #89

671011
13948
121651
321514

Solution #90

671110
12958
131641
321415

Solution #91

67129
111058
131632
411415

Solution #92

69127
154114
316132
105811

Solution #93

69154
127114
316105
132811

Solution #94

610117
153214
416131
95812

Solution #95

610153
117214
41695
131812

Solution #96

612133
155410
21697
111814

Solution #97

612133
105415
71692
111814

Solution #98

613114
123514
716101
92815

Solution #99

613123
114514
71692
101815

Solution #100

711016
141343
111256
28159

Solution #101

711016
121453
131146
28159

Solution #102

711016
121453
641113
91582

Solution #103

711016
141235
111364
28159

Solution #104

711016
141235
461311
91582

Solution #105

711016
111346
141253
28159

Solution #106

711412
15946
101653
281113

Solution #107

721213
141118
91663
451510

Solution #108

721411
121318
91645
631510

Solution #109

741013
14938
111661
251512

Solution #110

741310
11968
141631
251215

Solution #111

74149
101338
111625
611512

Solution #112

751210
11968
141631
241315

Solution #113

761011
12958
131641
231514

Solution #114

76129
101158
131623
411514

Solution #115

79126
144115
216133
115810

Solution #116

79144
126115
216115
133810

Solution #117

710152
145411
11698
123613

Solution #118

711106
142315
416131
95812

Solution #119

711142
106315
41695
131812

Solution #120

713104
122515
616111
93814

Solution #121

713122
104515
61693
111814

Solution #122

714112
133612
41695
101815

Solution #123

714112
123613
51694
101815

Solution #124

811213
151036
91654
271411

Solution #125

811213
141127
91654
361510

Solution #126

811411
151054
91636
271213

Solution #127

811411
121327
91636
541510

Solution #128

811510
141154
91627
361213

Solution #129

811510
121336
91627
541411

Solution #130

821113
15946
101653
171412

Solution #131

821311
15964
101635
171214

Solution #132

82159
131164
101617
351214

Solution #133

82159
111346
101617
531412

Solution #134

82159
101167
131614
351214

Solution #135

82159
101347
111616
531412

Solution #136

831013
14947
111652
161512

Solution #137

831310
14974
111625
161215

Solution #138

83149
131074
111616
251215

Solution #139

83149
111076
131614
251215

Solution #140

83149
111346
101617
521512

Solution #141

83149
101347
111616
521512

Solution #142

851011
12967
131632
141514

Solution #143

851110
12976
131623
141415

Solution #144

85129
131074
111616
231415

Solution #145

85129
131164
101617
321514

Solution #146

85129
111076
131614
231415

Solution #147

85129
101167
131614
321514

Solution #148

89125
152314
116134
107611

Solution #149

89125
143215
116134
116710

Solution #150

89143
152512
116116
107413

Solution #151

89143
125215
116116
134710

Solution #152

89152
143512
116107
116413

Solution #153

89152
125314
116107
134611

Solution #154

810115
151414
216133
97612

Solution #155

810115
141415
316132
97612

Solution #156

810133
151612
216115
97414

Solution #157

810133
121615
516112
97414

Solution #158

810151
133612
21697
115414

Solution #159

810151
115414
21697
133612

Solution #160

811105
151414
216133
96712

Solution #161

811105
141415
316132
96712

Solution #162

811132
141712
316105
96415

Solution #163

811132
121714
516103
96415

Solution #164

811141
132712
31696
105415

Solution #165

811141
105415
31696
132712

Solution #166

813103
151612
216115
94714

Solution #167

813103
121615
516112
94714

Solution #168

813112
141712
316105
94615

Solution #169

813112
121714
516103
94615

Solution #170

813121
112714
51694
103615

Solution #171

813121
103615
51694
112714

Solution #172

91816
151252
471013
614113

Solution #173

91816
141253
461113
715102

Solution #174

91816
157210
612133
414115

Solution #175

91816
412513
157102
614113

Solution #176

91816
412513
146113
715102

Solution #177

92158
141163
716110
451213

Solution #178

92158
121345
716110
631411

Solution #179

92158
711610
141613
451213

Solution #180

92158
713410
121615
631411

Solution #181

93148
121345
716110
621511

Solution #182

93148
713410
121615
621511

Solution #183

94147
121336
516211
811510

Solution #184

94147
613312
111625
811510

Solution #185

95128
141163
716110
421513

Solution #186

95128
711610
141613
421513

Solution #187

95128
142315
416131
711610

Solution #188

97126
151414
216133
810511

Solution #189

97126
141415
316132
810511

Solution #190

97144
151612
216115
810313

Solution #191

97144
121615
516112
810313

Solution #192

91168
142315
416131
751210

Solution #193

91276
151414
216133
851011

Solution #194

91276
141415
316132
851011

Solution #195

91474
151612
216115
831013

Solution #196

91474
121615
516112
831013

Solution #197

101716
81592
136411
312145

Solution #198

101716
81592
114613
514123

Solution #199

101716
15829
613114
312145

Solution #200

101716
15829
411136
514123

Solution #201

101158
121336
516211
74149

Solution #202

101158
613312
111625
74149

Solution #203

102157
113614
81691
513412

Solution #204

103813
156112
516112
49147

Solution #205

103156
813112
51649
112147

Solution #206

104713
155212
616111
39148

Solution #207

104137
15982
616111
351214

Solution #208

104137
69811
151612
351214

Solution #209

104155
713212
61639
111148

Solution #210

105811
154114
316132
69127

Solution #211

105118
69712
151621
341413

Solution #212

105127
15982
616111
341314

Solution #213

105127
69811
151612
341314

Solution #214

105127
152314
116134
81169

Solution #215

105154
811114
31669
132127

Solution #216

106711
153214
416131
59128

Solution #217

106153
131812
41695
711214

Solution #218

106153
121813
51694
711214

Solution #219

106153
711214
41659
131128

Solution #220

108115
15964
216313
711412

Solution #221

108115
49615
131632
711412

Solution #222

101167
152314
116134
85129

Solution #223

101176
85912
131641
321415

Solution #224

101185
76912
131632
411415

Solution #225

101347
113614
81691
521512

Solution #226

101374
83914
111661
521215

Solution #227

101383
74914
111652
611215

Solution #228

101563
131812
41695
721114

Solution #229

101563
121813
51694
721114

Solution #230

101563
112714
51694
811213

Solution #231

111616
81493
137410
212155

Solution #232

111616
81493
104713
515122

Solution #233

111616
14839
713104
212155

Solution #234

111616
14839
410137
515122

Solution #235

112813
147112
516103
49156

Solution #236

112147
813112
51649
103156

Solution #237

112156
14983
516112
471013

Solution #238

112156
101347
516112
83149

Solution #239

112156
59812
141613
471013

Solution #240

112156
513412
101617
83149

Solution #241

113146
101347
516112
82159

Solution #242

113146
513412
101617
82159

Solution #243

113146
102715
81691
513412

Solution #244

114613
145312
716101
29158

Solution #245

114136
751012
141631
29815

Solution #246

114145
613312
71629
101158

Solution #247

115810
144115
216133
79126

Solution #248

115108
151414
216133
61279

Solution #249

115108
141415
316132
61279

Solution #250

115144
151810
21697
612313

Solution #251

115144
101815
71692
612313

Solution #252

115144
810115
21679
133126

Solution #253

117610
142315
416131
59128

Solution #254

117106
14983
516112
421513

Solution #255

117106
59812
141613
421513

Solution #256

117142
610315
41659
131128

Solution #257

118105
14974
316213
611512

Solution #258

118105
49714
131623
611512

Solution #259

11986
751012
141631
241315

Solution #260

111058
151414
216133
67129

Solution #261

111058
141415
316132
67129

Solution #262

111067
85912
131641
231514

Solution #263

111085
67912
131623
411514

Solution #264

111346
102715
81691
531412

Solution #265

111364
82915
101671
531214

Solution #266

111382
64915
101653
711214

Solution #267

111454
151810
21697
631213

Solution #268

111454
101815
71692
631213

Solution #269

111472
133108
41659
611215

Solution #270

111472
831013
91654
611215

Solution #271

121813
156310
51694
211147

Solution #272

121813
147211
51694
310156

Solution #273

121147
15694
516310
211813

Solution #274

121147
15964
216313
581110

Solution #275

121147
813211
516310
94156

Solution #276

121147
49615
131632
581110

Solution #277

121156
14794
516211
310813

Solution #278

121156
14974
316213
581011

Solution #279

121156
813310
516211
94147

Solution #280

121156
49714
131623
581011

Solution #281

122713
155410
61693
111148

Solution #282

122137
155104
61639
111814

Solution #283

122155
137104
616111
39814

Solution #284

122155
713410
616111
93148

Solution #285

122155
671011
131614
39814

Solution #286

122155
143611
11698
713410

Solution #287

122155
613411
716110
93148

Solution #288

123613
145411
71692
110158

Solution #289

123136
145114
71629
110815

Solution #290

123145
136114
716110
29815

Solution #291

123145
761110
131614
29815

Solution #292

123145
152710
11698
613411

Solution #293

123145
713410
616111
92158

Solution #294

123145
613411
716110
92158

Solution #295

12589
152314
116134
611107

Solution #296

12589
143215
116134
710116

Solution #297

125143
15298
116710
611413

Solution #298

125143
89215
116710
134116

Solution #299

125152
14398
116611
710413

Solution #300

125152
89314
116611
134107

Solution #301

12679
151414
216133
511108

Solution #302

12679
141415
316132
511108

Solution #303

126133
151108
21679
511414

Solution #304

126133
811015
91672
511414

Solution #305

126151
133108
216511
79414

Solution #306

126151
79414
216511
133108

Solution #307

12769
151414
216133
510118

Solution #308

12769
141415
316132
510118

Solution #309

127132
141118
31669
510415

Solution #310

127132
811114
91663
510415

Solution #311

127141
132118
316510
69415

Solution #312

127141
69415
316510
132118

Solution #313

12967
851011
131632
141514

Solution #314

12976
851110
131623
141415

Solution #315

12985
136114
716110
231415

Solution #316

12985
137104
616111
321514

Solution #317

12985
761110
131614
231415

Solution #318

12985
671011
131614
321514

Solution #319

121345
152710
11698
631411

Solution #320

121345
143611
11698
721510

Solution #321

121363
151108
21679
541114

Solution #322

121363
811015
91672
541114

Solution #323

121372
141118
31669
541015

Solution #324

121372
811114
91663
541015

Solution #325

121381
721114
91654
631015

Solution #326

121381
631015
91654
721114

Solution #327

131416
81295
117610
214153

Solution #328

131416
121075
68911
315142

Solution #329

131416
81295
106711
315142

Solution #330

131416
12859
711106
214153

Solution #331

131416
12859
610117
315142

Solution #332

131416
610711
12895
315142

Solution #333

131812
147211
31696
410155

Solution #334

131812
117214
61693
410155

Solution #335

131128
142711
41695
315610

Solution #336

132811
127114
316105
69154

Solution #337

132127
811114
31669
105154

Solution #338

132154
12985
316114
671011

Solution #339

132154
101167
316114
85129

Solution #340

132154
39814
121615
671011

Solution #341

132154
311614
101617
85129

Solution #342

133612
115414
81691
210157

Solution #343

133810
126115
216115
79144

Solution #344

133108
151612
216115
41479

Solution #345

133108
121615
516112
41479

Solution #346

133126
151810
21697
414511

Solution #347

133126
101815
71692
414511

Solution #348

133126
810115
21679
115144

Solution #349

133144
115126
81619
210715

Solution #350

133144
85129
111616
210715

Solution #351

133144
89215
116710
126115

Solution #352

134143
12976
116215
851110

Solution #353

135124
101167
316114
82159

Solution #354

135124
311614
101617
82159

Solution #355

136411
123514
716101
29158

Solution #356

136114
89215
116710
123145

Solution #357

136123
411514
71629
101158

Solution #358

137410
122515
616111
39148

Solution #359

137104
12985
316114
621511

Solution #360

137104