Build Your Own Sloop: Motherboard (9x9)
(Published on 9. August 2024, 10:30 by Playmaker6174)
Let's just get straight into the thing.
(Setter note: it's easy to make some mistakes/false assumptions with this kind of concept so careful notations are highly recommended)
Rules:
- Normal 9x9 Sudoku rules apply: every row, column and 3x3 box contains digits from 1 to 9 each once.
- Draw a one-cell wide loop that travels orthogonally through some cells in the 9x9 grid. The loop doesn't intersect itself but may touch itself at some points (orthogonally or diagonally).
LOOP VARIANT: Along the loop, orthogonally adjacent digits must alternate between low digit {1,2,3,4} and high digit {6,7,8,9}. For the sake of this puzzle, digit 5 will NEVER lie on the loop.
- A digit in a cell with blue arrow[s] indicates the combined amount of cells along the indicated direction[s] that belong to the loop, not including itself.
- A digit in a cell with red arrow[s] indicates the combined amount of cells along the indicated direction[s] that DO NOT belong to the loop, not including itself.
(N.B: a cell with arrow[s] may or may not belong to the loop)
- An outside clue of a row/column shows how many grid edges the loop goes through within that row/column. For such case, a grid edge is considered as the edge shared by two orthogonally adjacent cells in a row/column (and this doesn't include the overall 9x9 grid border).
Puzzle: Penpa plus - Sudokupad
The answer check in penpa link will trigger once all digits are correctly filled, as well as the loop being correctly drawn.
Good luck and have fun solving!
Solution code: Enter the digits that are on the loop in row 3 and then row 4. (enter from left to right for each row)
Comments
on 9. August 2024, 22:10 by bansalsaab
That was crazy. Wasnt sure if I am on the right path. Some mistakes along the way but very slow and logical.
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Thank you for solving and the feedback! You can left a hidden comment over here about the parts you weren’t certain about, I may try to point out the intended things from there.
on 9. August 2024, 19:33 by Volkner
Looks like a fun idea, but I just don't understand what is meant by the grid edge rule. Could you provide an example?
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Hi there, so for example, if the loop travels from R4C4 to R4C5, it counts as one grid edge. So if it crosses a boundary between two orthgonally adjacent cells, it counts as ‘one grid edge’.
on 9. August 2024, 17:04 by PierreTombal
Amazing puzzle...
About the loop only moving orthogonally, I believe that is implied by the high/low alternating rule. The rule that I had to read multiple times was about the "grid edges", I think it would be better understandable if you referred to this as crossing cell boundaries in that row or column.
on 9. August 2024, 11:54 by Bankey
Can it be assumed that the loop travels between two cells only orthogonally (not mentioned explicitly in the rules), or is that something to be deciphered by the solver?
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Ah, the loop only goes orthogonally in this case, I may add it in for better clarification.
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Thanks, Playmaker :).
on 9. August 2024, 10:40 by Niverio
Very lovely logic throughout! Pretty smooth after the tricky opening too.
