Logic Masters Deutschland e.V.

I set this puzzle inspired by the great cycle-series by SirSchmoopy, which need in my opinion much more attention and solves.

- Normal Sudoku rules apply.
- In cages, digits must sum to the small clue in the top left corner of the cage. Digits cannot repeat within a cage.
- Black dots join cells with a 1:2 ratio. Not all dots are given.
- X-Cycle rules apply.

Cycle:

Let a 'cycle' be the loop in a single row/column in a grid created by repeatedly going from a digit to the column/row indexed by that digit in the same row/column. For instance, if a cell contained the digit 2, the next cell in the cycle would be the cell in column 2 for that row. Then, if column 2 had a 4 as its digit, the next cell in the cycle would be the cell in column 4 and so on.

Order:

Let the 'order' of a cycle be the number of unique cells in a cycle. For instance, if column 7 contained a 3, and column 3 contained a 7, this would create an order 2 cycle.

Additional words:

Cycles cannot partially overlap. A cell is only ever part of a single cycle. The order of all unique cycles in a row/column always sums to 9. A cycle can have an order of 1 if, and only if, the digit in a cell is the same as the cell's column/row number. This means you can remove some candidates in a row that would create an order 1 cycle in situations where you already know there are cycles in the row/column that sum to 9. For a specific example, if there's an order 9 cycle in a row, then column 1 in that row cannot be 1, column 2 cannot be a 2, column 3 cannot be a 3 etc.

X-Cycle:

The digits in row 1 and column 1 are all equal to their cell's order (X). E.g. if the digit in column 1 is 3, we know automatically that this cell is part of an order 3 cycle, so there are 2 other digits (e.g. 8 in column 3 and 1 in column 8) in that row/cycle.

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