Cycle Killer Redux

(Eingestellt am 12. Oktober 2026, 22:52 Uhr von SirSchmoopy)

Rules:

Normal sudoku rules apply.

Normal killer sudoku rules apply. Digits in a cage cannot repeat and sum to the total indicated in the top left corner.

Cycles: In each row, every digit points to another cell in the same row: e.g. -a 3 points to the cell in column 3 Start anywhere and follow the pointers, and you'll always arrive back where you started. The cells you pass through form a cycle, and the number of cells in it is the cycle's order. A cell's order is the order of the cycle it belongs to. e.g. - A 5 in column 5 points to itself, so it's cell is of order 1.

Cages: Along with regular killer sudoku rules, the orders of the cells in a cage must not repeat and must also sum to the cage's clue. A single-cell cage without a clue contains a digit equal to that cell's order.

Example:

See below for a valid and invalid killer cage under this additional cycle killer constraint.

In the first (valid) example, the order of the 4 in R2 is 1 (4 is in column 4 so it points to itself). The 2 in R3 is in an order 5 cycle (2 -> 3 ->5 -> 7 -> 4) and 4+2=1+5=6

The second example is invalid for two reasons:

The 1 is in an order 3 cycle. This immediately makes the cage invalid as the order of the other cycle would have to be 3 in order to sum to 6, and orders cannot repeat within cages.
The 5 is in a cycle with an order of at least 4, so the sum of the orders in the cage is at least 3+4=7. To show the cycle is an order of at least 4, consider the following:
The 5 is in the 6th column, so the 5 and the 6 are part of the cycle.
The 6 is in the 7th column which means the 7 is part of the cycle.
The 7 is in the 3rd column, so the 3 in that row is part of the cycle as well.
The smallest cycle is then order 4 by placing a 3 in R6C5.