4x4 sudoku: A Simpler Sudoku


Introduction

There are many different sudoku variations. 4x4 sudoku is one of them. It has four rows, four columns and four boxes where the classic version has nine rows, nine columns and nine boxes. The 4x4 version is often called "sudoku for kids" because they are much simpler puzzles to solve.

Get the Dry-Erase Version of 4x4

See the 4x4 sudoku board with dry erase surface you can play for hours. Available now in the online store.

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User's Guide

If you purchased the 4x4 dry erase board and misplaced the user's guide you can find it here.

Combinations

It took mathemeticians a long time to come up with the total number of valid 9x9 sudoku combinations. And there are a lot of them - 6,670,903,752,021,072,936,960 to be exact. Go to the Sudoku Research page for more information.

4x4 Combinations

There are however far fewer valid 4x4 sudoku combinations. A program was written to manually go through all of the possible numbers and make a list of all valid ones. The program "brute force" reads all of the four billion numbers and checks each one to see if it makes a valid puzzle. Every number that is "valid" is put in a list. The program takes about 1/2 hour to run.

How to find all of the valid 4x4 combinations. Imagine a sudoku grid with 16 cells and picture in your mind a grid with all 1's in it. Then imagine counting from 1111 1111 1111 1111 to 4444 4444 4444 4444. There are 4,294,967,296 (a little over four billion) numbers in that range. But how many of those numbers can be valid sudoku puzzles? For example it is obvious that 1111 1111 1111 1111 can't make a valid sudoku puzzle.

It turns out there are 288 of the four billion plus numbers that make valid sudoku puzzles. Here is a list of all 288 numbers.

If you purchased the 4x4 board with dry erase surface you can use this list of valid numbers to write on the board. Only write a few numbers from one of the 288 combinations in the list and see if you can solve it. If it's solvable it's ready to give to someone to try.



Puzzle #

Values

Puzzle #

Values

1

1234 3412 2143 4321

145

3124 2413 1342 4231

2

1234 3412 2341 4123

146

3124 2413 4231 1342

3

1234 3412 4123 2341

147

3124 2431 1243 4312

4

1234 3412 4321 2143

148

3124 2431 1342 4213

5

1234 3421 2143 4312

149

3124 2431 4213 1342

6

1234 3421 4312 2143

150

3124 2431 4312 1243

7

1234 4312 2143 3421

151

3124 4213 1342 2431

8

1234 4312 3421 2143

152

3124 4213 1432 2341

9

1234 4321 2143 3412

153

3124 4213 2341 1432

10

1234 4321 2413 3142

154

3124 4213 2431 1342

11

1234 4321 3142 2413

155

3124 4231 1342 2413

12

1234 4321 3412 2143

156

3124 4231 2413 1342

13

1243 3412 2134 4321

157

3142 2413 1234 4321

14

1243 3412 4321 2134

158

3142 2413 1324 4231

15

1243 3421 2134 4312

159

3142 2413 4231 1324

16

1243 3421 2314 4132

160

3142 2413 4321 1234

17

1243 3421 4132 2314

161

3142 2431 1324 4213

18

1243 3421 4312 2134

162

3142 2431 4213 1324

19

1243 4312 2134 3421

163

3142 4213 1324 2431

20

1243 4312 2431 3124

164

3142 4213 2431 1324

21

1243 4312 3124 2431

165

3142 4231 1324 2413

22

1243 4312 3421 2134

166

3142 4231 1423 2314

23

1243 4321 2134 3412

167

3142 4231 2314 1423

24

1243 4321 3412 2134

168

3142 4231 2413 1324

25

1324 2413 3142 4231

169

3214 1423 2341 4132

26

1324 2413 3241 4132

170

3214 1423 4132 2341

27

1324 2413 4132 3241

171

3214 1432 2143 4321

28

1324 2413 4231 3142

172

3214 1432 2341 4123

29

1324 2431 3142 4213

173

3214 1432 4123 2341

30

1324 2431 4213 3142

174

3214 1432 4321 2143

31

1324 4213 2431 3142

175

3214 4123 1342 2431

32

1324 4213 3142 2431

176

3214 4123 1432 2341

33

1324 4231 2143 3412

177

3214 4123 2341 1432

34

1324 4231 2413 3142

178

3214 4123 2431 1342

35

1324 4231 3142 2413

179

3214 4132 1423 2341

36

1324 4231 3412 2143

180

3214 4132 2341 1423

37

1342 2413 3124 4231

181

3241 1423 2134 4312

38

1342 2413 4231 3124

182

3241 1423 2314 4132

39

1342 2431 3124 4213

183

3241 1423 4132 2314

40

1342 2431 3214 4123

184

3241 1423 4312 2134

41

1342 2431 4123 3214

185

3241 1432 2314 4123

42

1342 2431 4213 3124

186

3241 1432 4123 2314

43

1342 4213 2134 3421

187

3241 4123 1432 2314

44

1342 4213 2431 3124

188

3241 4123 2314 1432

45

1342 4213 3124 2431

189

3241 4132 1324 2413

46

1342 4213 3421 2134

190

3241 4132 1423 2314

47

1342 4231 2413 3124

191

3241 4132 2314 1423

48

1342 4231 3124 2413

192

3241 4132 2413 1324





Puzzle #

Values

Puzzle #

Values

49

1423 2314 3142 4231

193

3412 1234 2143 4321

50

1423 2314 3241 4132

194

3412 1234 2341 4123

51

1423 2314 4132 3241

195

3412 1234 4123 2341

52

1423 2314 4231 3142

196

3412 1234 4321 2143

53

1423 2341 3214 4132

197

3412 1243 2134 4321

54

1423 2341 4132 3214

198

3412 1243 4321 2134

55

1423 3214 2341 4132

199

3412 2134 1243 4321

56

1423 3214 4132 2341

200

3412 2134 4321 1243

57

1423 3241 2134 4312

201

3412 2143 1234 4321

58

1423 3241 2314 4132

202

3412 2143 1324 4231

59

1423 3241 4132 2314

203

3412 2143 4231 1324

60

1423 3241 4312 2134

204

3412 2143 4321 1234

61

1432 2314 3241 4123

205

3421 1234 2143 4312

62

1432 2314 4123 3241

206

3421 1234 4312 2143

63

1432 2341 3124 4213

207

3421 1243 2134 4312

64

1432 2341 3214 4123

208

3421 1243 2314 4132

65

1432 2341 4123 3214

209

3421 1243 4132 2314

66

1432 2341 4213 3124

210

3421 1243 4312 2134

67

1432 3214 2143 4321

211

3421 2134 1243 4312

68

1432 3214 2341 4123

212

3421 2134 1342 4213

69

1432 3214 4123 2341

213

3421 2134 4213 1342

70

1432 3214 4321 2143

214

3421 2134 4312 1243

71

1432 3241 2314 4123

215

3421 2143 1234 4312

72

1432 3241 4123 2314

216

3421 2143 4312 1234

73

2134 3412 1243 4321

217

4123 2314 1432 3241

74

2134 3412 4321 1243

218

4123 2314 3241 1432

75

2134 3421 1243 4312

219

4123 2341 1234 3412

76

2134 3421 1342 4213

220

4123 2341 1432 3214

77

2134 3421 4213 1342

221

4123 2341 3214 1432

78

2134 3421 4312 1243

222

4123 2341 3412 1234

79

2134 4312 1243 3421

223

4123 3214 1342 2431

80

2134 4312 1423 3241

224

4123 3214 1432 2341

81

2134 4312 3241 1423

225

4123 3214 2341 1432

82

2134 4312 3421 1243

226

4123 3214 2431 1342

83

2134 4321 1243 3412

227

4123 3241 1432 2314

84

2134 4321 3412 1243

228

4123 3241 2314 1432

85

2143 3412 1234 4321

229

4132 2314 1243 3421

86

2143 3412 1324 4231

230

4132 2314 1423 3241

87

2143 3412 4231 1324

231

4132 2314 3241 1423

88

2143 3412 4321 1234

232

4132 2314 3421 1243

89

2143 3421 1234 4312

233

4132 2341 1423 3214

90

2143 3421 4312 1234

234

4132 2341 3214 1423

91

2143 4312 1234 3421

235

4132 3214 1423 2341

92

2143 4312 3421 1234

236

4132 3214 2341 1423

93

2143 4321 1234 3412

237

4132 3241 1324 2413

94

2143 4321 1432 3214

238

4132 3241 1423 2314

95

2143 4321 3214 1432

239

4132 3241 2314 1423

96

2143 4321 3412 1234

240

4132 3241 2413 1324





Puzzle #

Values

Puzzle #

Values

97

2314 1423 3142 4231

241

4213 1324 2431 3142

98

2314 1423 3241 4132

242

4213 1324 3142 2431

99

2314 1423 4132 3241

243

4213 1342 2134 3421

100

2314 1423 4231 3142

244

4213 1342 2431 3124

101

2314 1432 3241 4123

245

4213 1342 3124 2431

102

2314 1432 4123 3241

246

4213 1342 3421 2134

103

2314 4123 1432 3241

247

4213 3124 1342 2431

104

2314 4123 3241 1432

248

4213 3124 1432 2341

105

2314 4132 1243 3421

249

4213 3124 2341 1432

106

2314 4132 1423 3241

250

4213 3124 2431 1342

107

2314 4132 3241 1423

251

4213 3142 1324 2431

108

2314 4132 3421 1243

252

4213 3142 2431 1324

109

2341 1423 3214 4132

253

4231 1324 2143 3412

110

2341 1423 4132 3214

254

4231 1324 2413 3142

111

2341 1432 3124 4213

255

4231 1324 3142 2413

112

2341 1432 3214 4123

256

4231 1324 3412 2143

113

2341 1432 4123 3214

257

4231 1342 2413 3124

114

2341 1432 4213 3124

258

4231 1342 3124 2413

115

2341 4123 1234 3412

259

4231 3124 1342 2413

116

2341 4123 1432 3214

260

4231 3124 2413 1342

117

2341 4123 3214 1432

261

4231 3142 1324 2413

118

2341 4123 3412 1234

262

4231 3142 1423 2314

119

2341 4132 1423 3214

263

4231 3142 2314 1423

120

2341 4132 3214 1423

264

4231 3142 2413 1324

121

2413 1324 3142 4231

265

4312 1234 2143 3421

122

2413 1324 3241 4132

266

4312 1234 3421 2143

123

2413 1324 4132 3241

267

4312 1243 2134 3421

124

2413 1324 4231 3142

268

4312 1243 2431 3124

125

2413 1342 3124 4231

269

4312 1243 3124 2431

126

2413 1342 4231 3124

270

4312 1243 3421 2134

127

2413 3124 1342 4231

271

4312 2134 1243 3421

128

2413 3124 4231 1342

272

4312 2134 1423 3241

129

2413 3142 1234 4321

273

4312 2134 3241 1423

130

2413 3142 1324 4231

274

4312 2134 3421 1243

131

2413 3142 4231 1324

275

4312 2143 1234 3421

132

2413 3142 4321 1234

276

4312 2143 3421 1234

133

2431 1324 3142 4213

277

4321 1234 2143 3412

134

2431 1324 4213 3142

278

4321 1234 2413 3142

135

2431 1342 3124 4213

279

4321 1234 3142 2413

136

2431 1342 3214 4123

280

4321 1234 3412 2143

137

2431 1342 4123 3214

281

4321 1243 2134 3412

138

2431 1342 4213 3124

282

4321 1243 3412 2134

139

2431 3124 1243 4312

283

4321 2134 1243 3412

140

2431 3124 1342 4213

284

4321 2134 3412 1243

141

2431 3124 4213 1342

285

4321 2143 1234 3412

142

2431 3124 4312 1243

286

4321 2143 1432 3214

143

2431 3142 1324 4213

287

4321 2143 3214 1432

144

2431 3142 4213 1324

288

4321 2143 3412 1234




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