The Winding Path to Infinity
(Published on 11. September 2026, 20:54 by Kjupatrick)
The Winding Path to Infinity by Patrick Junke
Rules:
Standard Sudoku rules apply.
(Place the digits 1–9 exactly once in each row, column, and 3×3 box.)
Each line has a beginning and an end, neither of which is indicated.
Each cell on a line has an associated value. Starting from the beginning of a line, each cell's value is twice that of the previous cell.
The digit in each cell on a line is the digital root of its value: repeatedly add its digits together until a single digit from 1 to 9 remains.
For example, a cell with value 32 contains 5 (3 + 2 = 5). The next cell has value 64 and therefore contains 1 (6 + 4 = 10 → 1 + 0 = 1).
On each line, exactly one cell match its value.
Here is a link to a SudokuPad version of the grid.
Solution code: The nine digits of the last column, from top to bottom
Comments
on 17. September 2026, 19:43 by palletpusher
Very beautiful puzzle! I felt intimidated at first – not knowing off the top of my head e.g. 2^27 – but after iterating the sudoku digits under the repeated doubling and digital rooting operations, a very constrained set of patterns emerge.
After placing all the digits that clearly don't belong on the long line and fully colouring the rest of the grid, I pencil marked all the valid configurations based on the final "exactly one cell per line matches its value" rule, and everything disambiguated in very short order.
Very lovely! I quite enjoyed the colouring and learning a bit of maths trivia along the way. Thank you, Patrick!
Patrick> Thank you for your comment. It really made my day!
on 12. September 2026, 12:22 by Briks
Very nice puzzle, not hard at all when you see the logic, no guessing needed.
Patrick> Thanks Briks!
on 12. September 2026, 03:25 by Saltensity
What a nice puzzle, just a few bits of math observations required. I wonder if there's a more nicer way to unwind the long line without trial and error (the last part)?
Patrick> Thank you!
I understand that a sort of "trial and errors" may be required at first to understand the effets of the rules. But once the true mechanic is discovered, the number of options narrows down logically. If you make an other comment, whatever the content, I will be please to make it a hidden one and share with you the logic I found for the break of the long line.
