The Lost Sums of Akator
(Published on 21. April 2025, 12:00 by Oripy)
I designed these two puzzles to work together, with the values obtained from the first puzzle being the clues for the second. The first puzzle does not need input from the second puzzle to be solved.
Rules for Part 1:
- Normal 9x9 Sudoku rules apply.
- The cell with a grey circle must contain an odd digit
- Each red pill shape value is a two-digit number read from left to right or top to bottom
- Following the purple path from the top left to the bottom right, each red value is equal to the sum of the previous red value and the digits on the path leading to the red value
- Paths between red values are also Renban lines (cells within red pills do not count towards Renban lines). Digits on a Renban line form a set of non-repeating, consecutive digits in any order
- A "?" represents any number, including multi-digit numbers
Example:
The first puzzle:
Once you have solved this puzzle, take the numbers in the 9 red values in order along the path and use these values as the sums of the cages for the 2nd puzzle.
Rules for Part 2:
- Normal 9x9 Sudoku rules apply. Place the digits 1 to 9 exactly once in every row, column, and box
- Digits separated by a black dot have a 1:2 ratio, meaning one is exactly double the other
- X-Sums: Numbers in cages outside the grid indicate the sum of the first N digits, where N is the digit in the closest cell to the clue. These sums need to be determined by the solver
- Digits are from the 1-9 range only, no zero can appear anywhere in the puzzle (i.e. 10 is not a valid sum for an X-Sums)
- Digits in cages cannot repeat, including in multi-digit numbers. (i.e. if a cell in a cage contains the number 12, 1 and 2 cannot appear in any other cell of this cage, including 1X or 2X)
- Numbers in cages sum to the corresponding red values from the previous puzzle (numbered along the path, from top left to bottom right)
Example (values from the first example):
The second puzzle:

Second puzzle can be solved on
SudokuPad
Alternative link (replace [line 4 of part 1] with the 9 digits from line 4 of part 1):
https://tinyurl.com/lostsums-[line 4 of part 1]
Solution code: The digits on the 6th column of the second puzzle (9 digits).
Last changed on -
Solved by Briks, Da Letter El, MonsieurTRISTE, bansalsaab, yzyz, Fool on Hill, Piff, SPring, Clara123, skuntsel, h5663454, H1324851344, han233ing, functor, peacherwu2, AAAAAAAAAAAAAAAAAAA, rmn
Comments
Last changed on 27. April 2025, 08:54on 27. April 2025, 01:23 by skuntsel
What an adventure! It was an absolute treat to solve these puzzles, from start to finish. Amazing construct that unfolds really nicely, but only in case you think harder. The first puzzle is definitely on the harder spectrum, and really novel, but the second one is easier but it’s in reality a deceptive feeling, as it’s very unforgiving to the tiniest fault in the logic. Thank you for this stunning puzzle set, Oripy!
As a side note, it really pays off to turn down solution checking in harder puzzles as it definitely creates more incentives to do the work from the start. Let’s keep the newer puzzles without checks, or maybe create several versions.
> Thank you a lot for solving and the kind comment!
I also prefer solving puzzles with no solution checking.
Last changed on 23. April 2025, 01:15on 22. April 2025, 23:08 by Fool on Hill
Just the challenge I needed - great puzzle(s). It feels as if there is not enough to go on, but in both cases there somehow is.
> Thank you for the kind word!
on 22. April 2025, 03:46 by bansalsaab
That was crazy
Last changed on 21. April 2025, 23:15on 21. April 2025, 22:16 by Briks
Very nice and challenging!
> Thank you for solving! This puzzle was also challenging to create