Logic Masters Deutschland e.V.

0. Normal Sudoku Rules almost apply. Every row and column must contain the digits 1-9 exactly once as usual. However, in lieu of regions, the grid is broken entirely into omino shaped mini-regions, which must be discovered by the solver.

1. Digits may not repeat within an omino, however ominos of size less than 9 will not contain all 9 digits.

2. No two of these ominos have the same shape, including rotation and reflections as the same.  

3. Every omino contains a size clue, either one circle or one square. This cell contains the total number of cells in that omino.  

4. When the size clue is a circle, it gives the additional information that the total of all the cells in that omino is divisible by the size.  When the size clue is given in a square, the sum is not divisible by size.

Kropkiomino clues are given throughout the grid that express certain relationships between two cells:

5. A white kropkiomino clue between two cells indicates that those two cells contain consecutive numbers AND are part of the same omino.

6. A black kropkiomino clue between two cells indicates that those two cells contain numbers that have a ratio of 2:1 AND are part of different ominos.

7. All possible kropkiomino clues are given.  [To say that precisely, every pair of two adjacent consecutive digits which share an omino have a white kropki between them.  Every pair of two adjacent digits with a ratio of two to one that do not share an omino have a black kropki between them.]

Here is an example of a 6x6 grid that has been completed correctly.

Here is an example of a grid where many things have been done incorrectly. [Explanations of each error are given below.]

A) The 2 dominos are the same shape.  No two ominos in the puzzle can have the same shape.  

B) The red pentomino has a repeated 1. Ominos cannot contain repeated digits.

C) There is a white kropki is on the edge of the dark green pentomino. This is not correct. White kropki are always between cells in the same omino.

D) There are an adjacent 1 and 2 within the purple omino. This breaks the negative constraint. If two adjacent digits in the same omino are consecutive, there must be a white kropki between them.

E) Similarly, there is a 2 in purple and a 1 in dark yellow that are adjacent but do not have a black kropki between them, breaking the negative constraint on black kropki.

F) There are four cells that are not part of an omino. Every cell must be part of an omino, even if it is a monomino.

G) The dark blue omino in row one does not contain a circle or square. All ominos contain exactly one circle or exactly one square.

H) There is a black dot entirely within the yellow omino. Black dots only appear between cells in different ominos.

J) The purple omino has a circled 4, but its digits sum to 13, which is not divisible by 4.  In order for this to be acceptable, that circle would have to be a square.

K) The digit in the square of the light yellow omino is not equal to the size of the omino.

Have fun, leave a comment if you enjoy the puzzle!

Play this puzzle on f-puzzles