Kropki Sudoku

How to play kropki sudoku

Kropki sudoku puts dots between neighboring cells. A white dot means the two digits are consecutive, like 4 and 5. A black dot means one digit is double the other, like 3 and 6. A 1 and 2 could take either dot.

Black dots are the strongest clue: only 1, 2, 3, 4, 6 and 8 can sit on one, so 5, 7 and 9 never do. Some of our puzzles also use the negative rule, where a missing dot is a clue too.

Kropki sudoku: full lesson · Solving technique lesson

See the rule in 15 seconds

At a glance

• A white dot joins two consecutive digits, like 4 and 5.
• A black dot joins a digit and its double, like 3 and 6.
• 1 and 2 fit either dot.
• 5, 7 and 9 can never sit on a black dot.

Kropki dot chart

Every digit and what it can sit next to across each kind of dot. The black-dot column is the one to learn: it's short, and it decides most kropki break-ins.

Black-dot pairs: 1-2, 2-4, 3-6, 4-8. Two black dots in a straight line: 1-2-4 or 2-4-8. 1-2 is the only pair that fits both dots.

How to start a kropki sudoku

1. Clear 5, 7 and 9 off black dots

   Their doubles are too big and their halves aren't whole. That leaves 1, 2, 3, 4, 6 and 8 on every black dot.

2. Solve black-dot chains

   Two black dots in a straight line make a three-cell chain that can only be 1-2-4 or 2-4-8, with 2 or 4 in the middle. So the middle cell is 2 or 4 straight away.

3. Count white-dot runs

   Three white dots in a straight line are four consecutive digits in order, like 3-4-5-6, so the two middle cells can't be 1 or 9. A run of five always contains a 5.

4. Use the negative rule

   When all dots are given, neighbors without a dot are neither consecutive nor double. That often clears more candidates than the dots themselves. The kropki dots lesson practices it.

5. Watch 1 and 2

   They're the only pair that fits both dots, so a dot that could be either color often hides a 1-2 pair.

Common mistakes

Five levels, no guessing

Every puzzle has one solution, proved when it is set, and our solver finishes it by logic alone. The level is the hardest step the solve needs. Here is what each level asks of a kropki puzzle:

1. EasyClearing digits that can't sit on a dot, then singles.Play Easy
2. MediumTwo-cell dot logic: the pairs each dot allows, plus pointing pairs.Play Medium
3. HardDot chains and the negative rule, with pairs and triples.Play Hard
4. ExpertX-Wings, Skyscrapers and wings on top of the dots.Play Expert
5. FiendishChains and coloring, and testing every way a line of dots can be filled.Play Fiendish

The daily variant rotates through 11 kinds, so a kropki daily comes round about every 11 days. Past dailies

Hand-set kropki puzzles

Our levels are a good start. For more, Explore has 948 kropki puzzles made by people, from Logic Masters and Cracking the Cryptic. A few of the most popular:

RAT RUN 3: Double Dutchby marty_searsCrustby fuxiaThe Jugglerby H.BellOne Minute Puzzleby wucEarth, Wind and Fire Speed Runby Will PowerJust Kropkisby Hugo-BobMidnight snackby gUBBLORFirst Advent Sunday (Nala’s Advent(ures) Calendar 2023)by SandraNala

Setters with the most kropki puzzles:

• meggen033 97
• gwai77 27
• Will Power 26
• NotSoMagnifique 26
• lgastako 25
• Marty Sears 16
• pagedo 16
• GiAnMMV 15
• gUBBLOR 14
• Sudonym 14

Often combined with:

• Kropki + Killer 347
• Kropki + German Whispers 314
• Kropki + Renban 228
• Kropki + Fog of War 214
• Kropki + XV 182
• Kropki + Arrow 177
• Kropki + Thermo 166
• Kropki + Region Sum Lines 109
• Kropki + X-Sums 98
• Kropki + Ratio 70

All 948 kropki puzzles in Explore · Make your own kropki sudoku

Questions

More ways to play