Logic Masters Deutschland e.V.

• CTC
• F-Puzzles

• Normal sudoku rules apply.
• Normal killer sudoku rules apply. Digits in cages sum to the amount indicated by the clue in the top left corner of the cage. Digits cannot repeat within cages.

• Let a cycle be the loop of cells along a single row in the grid created by starting with a cell in column X with a digit of A, this A then 'points' to column A with a digit of B. This B then 'points' to column B with a digit of 'C'.... and so on until you get to a cell whose digit is X and points to the beginning where you started.
• Let the order of the cycle be the number of unique cells contained in that cycle

• In addition to normal killer sudoku rules, the orders of cycles in cages must sum to the amount indicated in the clue in the top left corner.
• In cases where no clue is given, the sum of the cage still equals the sum of the cycles within the cage.
• Orders cannot repeat within cages.

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

In the first (valid) example, the order of the 4 is 1 (4 is in column 4 so it points to itself). The 2 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.