Normal sudoku rules apply. In cages, digits must sum to the small clue given in the top left corner of the cage (if given). Digits cannot repeat within a cage. Cells separated by a white dot contain consecutive digits. Cells separated by a black dot contain digits in a ratio of 2:1. Not all possible dots are given. Digits in circles are equal to the reduced sum of the digits along their arrows. The sum of the digits on any arrow must be a 2-digit number. Arrows connected to the same circle never have the same sum. Digits may repeat along an arrow if allowed by other rules.
A reduced sum is calculated by taking the digit(s) of the actual sum and adding them together.
For example, the reduced sum of 24 is 6 as 2+4=6.
If the reduced sum is initially a 2-digit number, the process repeats until there is only 1 digit. For example, the reduced sum of 74 is 2 as 7+4=11 and 1+1=2.
Link: f-puzzles
Solution code: Rows 2 and 3 (18 digits, no commas or spaces)