A Very X-mas Snake
(Published on 25. December 2025, 06:20 by logicanimal)
Rules: X-Sum/XV variant
1. (Normal sudoku) Fill the grid with digits from 1-9 such that no digits repeat in each row/column/region.
2. (XV) If an edge is marked with an X, then the sum of the digits adjacent to the edge must be 10.
3. (X-sum) Numbers outside the grid represent the sum of the first x digits in that direction, where x is the digit in the first cell of that direction.
4. Furthermore, shade some cells to form a snake. The digit in the center of every region indicates how many cells are shaded in that region. A snake is an orthogonally connected path that never touches itself, not even diagonally.
5. The snake can be divided into disjoint segments such that the sums of each segment in order form an arithmetic sequence of length 3 or more. There may be multiple ways to segment the snake.
You can solve the puzzle here.
This is one of 12 disjoint puzzles I made this year with varying styles/difficulties themed around snakes and 2025.
Enjoy!
Solution code: Enter the arithmetic sequence that has the smallest starting number.
Comments
on 10. January 2026, 17:59 by logicanimal
@JustinTucker, thanks for catching that error. Glad you are enjoying the series!
on 10. January 2026, 17:56 by logicanimal
Corrected solution code. Thanks @JustinTucker
on 10. January 2026, 00:23 by logicanimal
@JustinTucker, sorry. Forgot to include that the arithmetic sequence should have length 3 or more. Thanks for spotting that.
on 10. January 2026, 00:21 by logicanimal
Clarified rule 5. The arithmetic sequence needs to have length 3 or more.
on 8. January 2026, 23:24 by JustinTucker
Could you please elaborate over rule 5 and the solution code? Since sequences of length one or two are always "arithmetic" rule 5 isn't a real constraint. And the smallest starting point would be head or tail of the snake.
I just solved the puzzle using rules 1-4 and tried all feasible arithmetic sequences to get the solution code.
on 27. December 2025, 12:17 by PierreTombal
I fear that `an arithmetic sequence` is beyond me. Nothing stands out. Thank you for the puzzle anyway.
on 25. December 2025, 23:54 by Ragna
Sorry, I am not familiar with penpa.
