The Underneath
(Published on 13. March 2024, 14:01 by vitaminz)
RULES:
NON-NORMAL SUDOKU - Place the digits 0-8 once each in every row, column, and 3x3 box.
RENBAN - Digits on a pink line form a non-repeating consecutive set in any order.
SECRET GRID - There is a secret grid behind the normal grid, which is also a valid sudoku using the digits 0-8, with Renban lines in exactly the same places as the normal grid. Digits in the secret grid are equal to the digit in the corresponding cell in the normal grid plus that cell's row and column numbers, mod 9. "Mod 9" means that you take the remainder of that number after it is divided by 9. Equivalently, it is the result you get after subtracting 9 until the number is less than 9. For example, there is a 5 in r5c1. In the secret grid, there must be a (5 + 5 + 1) mod 9 = 2.
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A suggestion: It is possible to solve this puzzle by opening a blank grid and constructing the secret grid alongside the main grid. This may even be easier than the intended path. However, I strongly advise against this, as I believe it will result in a rather tedious solve. If you are stuck, I have provided some hints below, with each line getting more specific.
Training: If you would like to try the secret grid constraint in a smaller puzzle, I have created a 5x5 Latin Square (sudoku without regions) that includes that constraint:
Below are some hints in hidden text if you would like them (highlight the white space to see them). They get progressively more explicit. They would also help with the Latin Square.
I've told you not to construct the secret grid, but it is a very important constraint.
If there were no renbans in the puzzle, I would never have to calculate a digit in the secret grid to solve it.
Try to reframe the secret grid constraint in terms of features of the main grid only (ignoring renbans).
Positive diagonals (from bottom left to top right) are very important. Particularly within boxes.
Watch Marty Sears and ThePedallingPianist
And check out a very different method in my solution guide
Solution code: Row 1 (top), from left to right (9 digits)
Comments
on 21. March 2024, 18:07 by vitaminz
Added video and solution guide links
on 16. March 2024, 17:19 by SamuPiano
Wonderful puzzle! Took me a while to wrap my head around the secret grid, but it is truly an original concept and perfectly executed!
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Thank you so much! -VitaminZ
on 14. March 2024, 23:35 by Abdul the Killer
Beautiful puzzle guys, bravo! The secret grid rule is beautifully bonkers. Your advice was invaluable. I await more with anticipation.
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Thanks, ATK! You may be waiting a while but we'll see if more inspiration strikes -VitaminZ
on 13. March 2024, 20:18 by kublai
Once I got comfortable with my notation, the secrets unraveled rather nicely. Lovely puzzle!
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Thank you for the kind comment! -VitaminZ
on 13. March 2024, 14:41 by Abbott Abbott
There is some truly graceful logic in here that was incredibly satisfying to discover. Thank you for the advice on the secret grid! It is definitely more fun to not construct it.
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Thank you! It took a while to fit all the pieces together so I'm glad you found the intended discoveries :) --VitaminZ
