Kropki · Medium

No Dot in Kropki Sudoku

Every dot is shown, so two cells with no dot are neither one apart nor double: that rules digits out too.

The idea

Every dot is shown, so two side-by-side cells with no dot between them are neither one apart nor one double the other. That rules digits out as surely as a dot does.

A digit goes from a cell when everything left in the cell beside it, across an edge with no dot, is one apart from it, double it or half it. The fewer candidates the neighbour has, the more this finds.

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.

No dot between them

Medium puzzle · No Dot

There is no dot on the lit edge, so these two digits are not one apart, and neither is double the other.

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

Both cells lose a digit

Medium puzzle · No Dot

No dot on the lit edge, and both cells have only a few candidates left: each one limits the other.

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

Where it fits

MediumNo Dot is a Medium technique: Medium Kropki puzzles are the first to need it.

The Kropki overview explains the rule and the levels.

Try it on a Medium Kropki puzzle. Next Step points it out when it is the move.

The worked examples, every step

No dot between them

Medium Kropki puzzle · No Dot

  1. There is no dot on the lit edge, so these two digits are not one apart, and neither is double the other.
  2. Look at R1C2 and R1C3, side by side. No dot: the two digits are neither one apart nor one double the other.
  3. Beside a 3 with no dot, R1C3 cannot be 2, 4 or 6 (one apart, double or half) or another 3, and it can hold only 3, 4 and 6. So 3 cannot go in R1C2.
  4. Eliminate 3 from R1C2.
  5. Done: 3 is eliminated from R1C2.

Both cells lose a digit

Medium Kropki puzzle · No Dot

  1. No dot on the lit edge, and both cells have only a few candidates left: each one limits the other.
  2. Look at R2C2 and R2C3, side by side. No dot: the two digits are neither one apart nor one double the other.
  3. Beside an 8 with no dot, R2C3 cannot be 4, 7 or 9 (one apart, double or half) or another 8, and it can hold only 7, 8 and 9. So 8 cannot go in R2C2. Beside a 7 with no dot, R2C2 cannot be 6 or 8 (one apart, double or half) or another 7, and it can hold only 6, 7 and 8. So 7 cannot go in R2C3.
  4. Eliminate 8 from R2C2 and 7 from R2C3.
  5. Done: 8 is eliminated from R2C2; 7 is eliminated from R2C3.

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