Logic Masters Deutschland e.V.

Normal sudoku rules apply.

All clues work modulo 9.

White dots:

• Digits separated by a white dot must be consecutive, i.e. one of the digits is congruent to one more than the other digit modulo 9.
• Not all white dots are necessarily given.
• For example, 1 and 9 are consecutive, since 9 + 1 is congruent to 1 modulo 9.

Black dots:

• Digits separated by a black dot must be in a 2:1 ratio, i.e. one of the digits is congruent to twice the other digit modulo 9.
• Not all black dots are necessarily given.
• For example, 5 and 7 are in a 2:1 ratio, since 7 * 2 = 14, which is congruent to 5 modulo 9.

Red dots:

• Digits separated by a red dot must be BOTH consecutive AND in a 2:1 ratio.
• ALL possible red dots are given.

For clarity, two digits separated by a white dot are NOT in a 2:1 ratio and two digits separated by a black dot are NOT consecutive.

Killer cages:

• The sum of the digits in a cage is congruent to the digit in its top-left corner modulo 9.
• Digits may not repeat in a cage.

Play the puzzle here: SudokuPad