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 #ValuesPuzzle #Values
11234 3412 2143 43211453124 2413 1342 4231
21234 3412 2341 41231463124 2413 4231 1342
31234 3412 4123 23411473124 2431 1243 4312
41234 3412 4321 21431483124 2431 1342 4213
51234 3421 2143 43121493124 2431 4213 1342
61234 3421 4312 21431503124 2431 4312 1243
71234 4312 2143 34211513124 4213 1342 2431
81234 4312 3421 21431523124 4213 1432 2341
91234 4321 2143 34121533124 4213 2341 1432
101234 4321 2413 31421543124 4213 2431 1342
111234 4321 3142 24131553124 4231 1342 2413
121234 4321 3412 21431563124 4231 2413 1342
131243 3412 2134 43211573142 2413 1234 4321
141243 3412 4321 21341583142 2413 1324 4231
151243 3421 2134 43121593142 2413 4231 1324
161243 3421 2314 41321603142 2413 4321 1234
171243 3421 4132 23141613142 2431 1324 4213
181243 3421 4312 21341623142 2431 4213 1324
191243 4312 2134 34211633142 4213 1324 2431
201243 4312 2431 31241643142 4213 2431 1324
211243 4312 3124 24311653142 4231 1324 2413
221243 4312 3421 21341663142 4231 1423 2314
231243 4321 2134 34121673142 4231 2314 1423
241243 4321 3412 21341683142 4231 2413 1324
251324 2413 3142 42311693214 1423 2341 4132
261324 2413 3241 41321703214 1423 4132 2341
271324 2413 4132 32411713214 1432 2143 4321
281324 2413 4231 31421723214 1432 2341 4123
291324 2431 3142 42131733214 1432 4123 2341
301324 2431 4213 31421743214 1432 4321 2143
311324 4213 2431 31421753214 4123 1342 2431
321324 4213 3142 24311763214 4123 1432 2341
331324 4231 2143 34121773214 4123 2341 1432
341324 4231 2413 31421783214 4123 2431 1342
351324 4231 3142 24131793214 4132 1423 2341
361324 4231 3412 21431803214 4132 2341 1423
371342 2413 3124 42311813241 1423 2134 4312
381342 2413 4231 31241823241 1423 2314 4132
391342 2431 3124 42131833241 1423 4132 2314
401342 2431 3214 41231843241 1423 4312 2134
411342 2431 4123 32141853241 1432 2314 4123
421342 2431 4213 31241863241 1432 4123 2314
431342 4213 2134 34211873241 4123 1432 2314
441342 4213 2431 31241883241 4123 2314 1432
451342 4213 3124 24311893241 4132 1324 2413
461342 4213 3421 21341903241 4132 1423 2314
471342 4231 2413 31241913241 4132 2314 1423
481342 4231 3124 24131923241 4132 2413 1324




Puzzle #ValuesPuzzle #Values
491423 2314 3142 42311933412 1234 2143 4321
501423 2314 3241 41321943412 1234 2341 4123
511423 2314 4132 32411953412 1234 4123 2341
521423 2314 4231 31421963412 1234 4321 2143
531423 2341 3214 41321973412 1243 2134 4321
541423 2341 4132 32141983412 1243 4321 2134
551423 3214 2341 41321993412 2134 1243 4321
561423 3214 4132 23412003412 2134 4321 1243
571423 3241 2134 43122013412 2143 1234 4321
581423 3241 2314 41322023412 2143 1324 4231
591423 3241 4132 23142033412 2143 4231 1324
601423 3241 4312 21342043412 2143 4321 1234
611432 2314 3241 41232053421 1234 2143 4312
621432 2314 4123 32412063421 1234 4312 2143
631432 2341 3124 42132073421 1243 2134 4312
641432 2341 3214 41232083421 1243 2314 4132
651432 2341 4123 32142093421 1243 4132 2314
661432 2341 4213 31242103421 1243 4312 2134
671432 3214 2143 43212113421 2134 1243 4312
681432 3214 2341 41232123421 2134 1342 4213
691432 3214 4123 23412133421 2134 4213 1342
701432 3214 4321 21432143421 2134 4312 1243
711432 3241 2314 41232153421 2143 1234 4312
721432 3241 4123 23142163421 2143 4312 1234
732134 3412 1243 43212174123 2314 1432 3241
742134 3412 4321 12432184123 2314 3241 1432
752134 3421 1243 43122194123 2341 1234 3412
762134 3421 1342 42132204123 2341 1432 3214
772134 3421 4213 13422214123 2341 3214 1432
782134 3421 4312 12432224123 2341 3412 1234
792134 4312 1243 34212234123 3214 1342 2431
802134 4312 1423 32412244123 3214 1432 2341
812134 4312 3241 14232254123 3214 2341 1432
822134 4312 3421 12432264123 3214 2431 1342
832134 4321 1243 34122274123 3241 1432 2314
842134 4321 3412 12432284123 3241 2314 1432
852143 3412 1234 43212294132 2314 1243 3421
862143 3412 1324 42312304132 2314 1423 3241
872143 3412 4231 13242314132 2314 3241 1423
882143 3412 4321 12342324132 2314 3421 1243
892143 3421 1234 43122334132 2341 1423 3214
902143 3421 4312 12342344132 2341 3214 1423
912143 4312 1234 34212354132 3214 1423 2341
922143 4312 3421 12342364132 3214 2341 1423
932143 4321 1234 34122374132 3241 1324 2413
942143 4321 1432 32142384132 3241 1423 2314
952143 4321 3214 14322394132 3241 2314 1423
962143 4321 3412 12342404132 3241 2413 1324




Puzzle #ValuesPuzzle #Values
972314 1423 3142 42312414213 1324 2431 3142
982314 1423 3241 41322424213 1324 3142 2431
992314 1423 4132 32412434213 1342 2134 3421
1002314 1423 4231 31422444213 1342 2431 3124
1012314 1432 3241 41232454213 1342 3124 2431
1022314 1432 4123 32412464213 1342 3421 2134
1032314 4123 1432 32412474213 3124 1342 2431
1042314 4123 3241 14322484213 3124 1432 2341
1052314 4132 1243 34212494213 3124 2341 1432
1062314 4132 1423 32412504213 3124 2431 1342
1072314 4132 3241 14232514213 3142 1324 2431
1082314 4132 3421 12432524213 3142 2431 1324
1092341 1423 3214 41322534231 1324 2143 3412
1102341 1423 4132 32142544231 1324 2413 3142
1112341 1432 3124 42132554231 1324 3142 2413
1122341 1432 3214 41232564231 1324 3412 2143
1132341 1432 4123 32142574231 1342 2413 3124
1142341 1432 4213 31242584231 1342 3124 2413
1152341 4123 1234 34122594231 3124 1342 2413
1162341 4123 1432 32142604231 3124 2413 1342
1172341 4123 3214 14322614231 3142 1324 2413
1182341 4123 3412 12342624231 3142 1423 2314
1192341 4132 1423 32142634231 3142 2314 1423
1202341 4132 3214 14232644231 3142 2413 1324
1212413 1324 3142 42312654312 1234 2143 3421
1222413 1324 3241 41322664312 1234 3421 2143
1232413 1324 4132 32412674312 1243 2134 3421
1242413 1324 4231 31422684312 1243 2431 3124
1252413 1342 3124 42312694312 1243 3124 2431
1262413 1342 4231 31242704312 1243 3421 2134
1272413 3124 1342 42312714312 2134 1243 3421
1282413 3124 4231 13422724312 2134 1423 3241
1292413 3142 1234 43212734312 2134 3241 1423
1302413 3142 1324 42312744312 2134 3421 1243
1312413 3142 4231 13242754312 2143 1234 3421
1322413 3142 4321 12342764312 2143 3421 1234
1332431 1324 3142 42132774321 1234 2143 3412
1342431 1324 4213 31422784321 1234 2413 3142
1352431 1342 3124 42132794321 1234 3142 2413
1362431 1342 3214 41232804321 1234 3412 2143
1372431 1342 4123 32142814321 1243 2134 3412
1382431 1342 4213 31242824321 1243 3412 2134
1392431 3124 1243 43122834321 2134 1243 3412
1402431 3124 1342 42132844321 2134 3412 1243
1412431 3124 4213 13422854321 2143 1234 3412
1422431 3124 4312 12432864321 2143 1432 3214
1432431 3142 1324 42132874321 2143 3214 1432
1442431 3142 4213 13242884321 2143 3412 1234

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