Step Step Sums Sums
(Published on 24. April 2026, 00:00 by NXTMaster)
The rules are as follows:
- Inner 9x9 Sudoku: Place the digits 1-9 once in every row, column, and 3x3 box. Digits separated by a kropki must have a difference of 1 and digits on gray squares must be even.
- Inner Periodic Sums: All 36 cells bordering the Sudoku grid have a number equal to the sum of N and every Nth digit in the row/column moving away from the clue, where N is the first digit seen from the clue. Only digits within the Sudoku grid are taken into account.
- Outer Periodic Sums: Clues outside the inner periodic sums indicate the sum of N and every Nth digit in the row/column moving away from the clue and including the inner periodic sums, where N is the first digit seen from the clue. Double-digit inner clues are read as two single-digit numbers. Read the tens digit first when reading left to right/top to bottom and the ones digit first when reading right to left/bottom to top.
The puzzle is available on SudokuPad and Penpa (answer check only on digits within the Sudoku grid). Watch your step at the end!
Solution code: The nine digits of Row 7 in the Sudoku grid
Comments
on 26. April 2026, 10:51 by 6rank
Wow, only five stars out of five for difficulty. For me it felt even more difficult than that.
Nonetheless I somehow enjoyed the solve :)
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I'm glad to hear I managed to make a difficult yet enjoyable puzzle. Thank you for solving
on 24. April 2026, 21:38 by 6rank
[Edited conversation to make the clarification a public comment]
It seems I don't understand the example given.
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The rules may be a bit confusing, apologies. I mention "Moving away from the clue" to indicate direction, not starting point (clues at the bottom of the grid count going upward, ie away from the clue).
The steps start counting from the first digit seen by the clue, so an inner clue on the right side of row 7, for example, that sees a 2 in r7c9 would add the digits in r7c9, r7c7, r7c5, r7c3, and r7c1.
The reason why the Outer 15 clue in the example seems to count differently is that the inner clue of 16 needs to be read as two different digits. When the 15 clue sees the 6 of 16, the digits it steps over are the 1, 3, 1, 2, and 5, landing on the 9 (6th digit away from 6).
on 24. April 2026, 00:12 by Sotehr
It's an absolute honor that my pet constraint was the inspiration to such a wonderful puzzle.
I wish everyone careful counting!
