Logic Masters Deutschland e.V.

“Hierarchy” - A Domino Experiment

1. Sudoku: Place the digits 1-9 once each in every row, column, and 3x3 box.
2. Anti-Knight: Cells a knight’s move away from each other cannot contain the same digit.
3. Domino Clues:
   1. If a domino (pair of orthogonally adjacent cells) have a symbol of any kind between them, that domino is considered “clued.”
   2. Each type of clue has been placed in a hierarchy of ranks (See below).
   3. A clued domino will always display the highest rank clue possible (even if other clues would otherwise be valid).
   4. An “un-clued” domino may have any two digits, even if they would satisfy the conditions of a possible type of clue.
      
      

---

Example:

• A domino with a black dot between its two cells could contain the digits 2 and 4, but could not contain 1 and 2 because a 1-2 domino would also satisfy the White Kropki rule (a higher rank clue).
• A domino with no clue could contain a 1-2, a 2-4, or any other pair of digits, even though these pairings could satisfy the conditions of a type of clue. (Unclued = Unrestricted).

---

Hierarchy (Top to Bottom; So XV is the highest rank):

1. XV - Digits separated by an X sum to 10. Digits separated by a V sum to 5.
2. White Kropki - Digits separated by a white dot are consecutive.
3. Gray Kropki - If two digits are separated by a gray dot, one is 3 times the other.
4. Black Kropki - If two digits are separated by a black dot, one is 2 times the other.
5. German Dots - If two digits are separated by a green dot, they must differ by at least 5. 
6. Prime Sum - If two digits are separated by a P their sum must be a prime number.
7. Dutch Dots - If two digits are separated by a green dot, they must differ by at least 4.
8. Parity Dots - If two digits are separated by a red dot, they must be of different parity (one even and one odd).

Play on SudokuPad