Logic Masters Deutschland e.V.

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Definitions:

A cycle is the path along a single row in the grid formed by starting at any cell, then going to the cell in the column indexed by the first cell's digit, then the cell indexed by the second cell's digit etc. until you return to where you started

The order of a cycle is the number of unique digits in a cycle.

For a concrete example, if R1C1 was an 8, R1C8 was a 4, and R1C4 was a 1, this would form an order 3 cycle, as the 8 points to the 4, which points to a 1, which points back to the 8 at the beginning.

Rules:

Normal Sudoku rules apply.
Normal XV rules apply. Digits separated by an X sum to 10, and digits separated by a V sum to 5. Not all Xs and Vs are necessarily given.

In addition to normal XV rules, the orders of cycles of cells separated by a V sum to 5, and the orders of cycles separated by an X sum to 10.
Cycles separated by an X or a V are disjoint and do not overlap (so there could not be a single order 5 cycle that goes through both digits separated by a V)

Examples:

See below for some example clues valid under this constraint.

For the X clue, the order of the cycle of the 1 in R1C2 is 7, and the order of the 9 in R2C2 is 3, and 1+9=7+3=10

For the V clue, the order of the 2 in R4C5 is 2, and the order of the 3 in R5C5 is 3 and 2+3=2+3=5