Kropki · Easy

White and Black Dots in Kropki Sudoku

A digit stays beside a dot only if the cell across the dot can still hold its partner.

The idea

Two cells joined by a dot hold a matching pair: one apart across a white dot, one double the other across a black dot. So a digit can stay in a cell only if the cell across the dot can still hold its partner.

Some digits never have a partner. 5, 7 and 9 have no double or half from 1 to 9, so they can never sit on a black dot. Next Step calls these White Dot and Black Dot steps.

Worked examples

2 positions from real Kropki puzzles on this site, the familiar case first. Step through each one: the board lights what each step talks about, and the arrows show what rules what out.

A white dot

Easy puzzle · White Dot

Look at the lit white dot. Whatever goes on one side, the other side is one more or one less.

Step 1 of 5Step 2 of 5Step 3 of 5Step 4 of 5Step 5 of 5

A black dot

Easy puzzle · Black Dot

Look at the lit black dot. One side is double the other: 1 and 2, 2 and 4, 3 and 6, or 4 and 8.

Step 1 of 5Step 2 of 5Step 3 of 5Step 4 of 5Step 5 of 5

Where it fits

EasyWhite and Black Dots is an Easy technique: Easy Kropki puzzles are the first to need it.

The Kropki overview explains the rule and the levels.

Try it on an Easy Kropki puzzle. Next Step points it out when it is the move.

The worked examples, every step

A white dot

Easy Kropki puzzle · White Dot

  1. Look at the lit white dot. Whatever goes on one side, the other side is one more or one less.
  2. Look at R1C5 and R1C6, side by side. A white dot: the two digits are one apart.
  3. R1C6 can hold only 2, 3, 4 and 8, and none of them is one apart from 8. So 8 cannot go in R1C5. R1C5 can hold only 3, 4, 5 and 8, and none of them is one apart from 8. So 8 cannot go in R1C6.
  4. Eliminate 8 from R1C5 and R1C6.
  5. Done: 8 is eliminated from R1C5, R1C6.

A black dot

Easy Kropki puzzle · Black Dot

  1. Look at the lit black dot. One side is double the other: 1 and 2, 2 and 4, 3 and 6, or 4 and 8.
  2. Look at R2C2 and R2C3, side by side. A black dot: one digit is double the other (1 and 2, 2 and 4, 3 and 6, 4 and 8).
  3. 5 and 7 have no double or half from 1 to 9, so R2C2 cannot hold them. R2C3 can hold only 1, 3 and 6, and none of them is double or half of 8. So 8 cannot go in R2C2. R2C2 can hold only 5, 6, 7 and 8, and none of them is double or half of 1 or 6. So 1 and 6 cannot go in R2C3.
  4. Eliminate 5, 7 and 8 from R2C2 and 1 and 6 from R2C3.
  5. Done: 5, 7 and 8 are eliminated from R2C2; 1 and 6 are eliminated from R2C3.

Next: No Dot