Logic Masters Deutschland e.V.

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Normal Sudoku rules apply;

Cave: shade some cells such that all unshaded cells form one contiguous group, each contiguous group of shaded cells touches the edge of the grid, and no 2x2 area is fully shaded or fully unshaded;

3617173445: each '?' stands in for a different number form the set {3, 6, 17, 17, 34, 45}, each group (shaded or unshaded) contains at least one '?,' and the size of that group is determined by those numbers (it's size is the number of cells in the group). If a group contains one '?,' it's size is equal to the number it contains, if a group contains more than one '?,' its size is determined by concatenating all of the number it contains with the same mathematical operator (from +, -, ×, or ÷) and resolving the equation. For example, a group containing three '?'s could have the size '3 + 6 + 34 = 43' but not '6 × 34 ÷ 3 = 68;'

BYO Killer Cages: for each '?,' draw a cage of contiguous cells such that the '?' is both the topmost and the leftmost cell in the cage. Digits may not repeat in cages, cages may not overlap, and the sum of the shaded digits in the cage is given by the '?;'

Ratio Kropki: adjacent cells within a shaded region may not have a 2:1 ratio unless they are separated by a white dot, in which case they must have a 2:1 ratio;

Difference Kropki: adjacent cells within the unshaded region may not be consecutive unless they are separated by a white dot, in which case they must be consecutive.

(dots that separate a shaded cell and an unshaded cell have no restriction)