Penumbra (Shadow Sums Sudoku)
(Published on 19. June 2025, 10:56 by Feadoor)
Normal Sudoku rules apply: place a number from 1 to 9 into each cell so that every row, column and box contains each number exactly once.
Shadow sums: A clue outside the grid gives the sum of all numbers in that row/column which are smaller than the number immediately before them, when reading from the direction of the clue.
For example, if a row contains the numbers 463752891, then the correct sum would be 3 + 5 + 2 + 1 = 11 from the left, and 8 + 2 + 3 + 4 = 17 from the right.
Solution code: Column 5, top to bottom
Comments
on 28. June 2025, 07:42 by marcmees
Very nice. altough same rules, the solving technique feels completely different from the second one. Thanks
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Sam says: Well done on the solve!
on 28. June 2025, 03:33 by Jackler
Very hard to grasp this logic. I have never seen this rule and it took me a while to understand it. Very difficult to look from both sides, but very elegant.
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Sam says: Thanks for solving!
on 26. June 2025, 16:38 by Feadoor
Penpa link added
on 22. June 2025, 00:18 by Piatato
Excellent! Really fun puzzle, thanks!
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Sam says: Thank you for solving - glad you enjoyed it!
on 20. June 2025, 22:02 by Franjo
Hard, but once you get some of the basic deductions of this unusual constraint - well, that took more than an hour of my time, at least. Great math-puzzle! Thank you very much for creating and sharing this wonderful thing.
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Sam says: Thank you for the kind words! Well done on making it through.
on 19. June 2025, 11:26 by Mr.Menace
Very interesting variant and a nice application of it with cool logic
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Sam says: Thank you for solving and for putting up with the first version!
