Plumber
(Published on 8. October 2023, 18:52 by Lyun Licuss)
In the puzzle world, there is a room with size "9×9", filled with a network of horizontal and vertical connected pipes. These pipelines are systematically divided into three groups:
Group 1: The Odd Numbers as 1,3,5,7,9
Group 2: The Large Numbers as 5,6,7,8,9
Group 3: The Non Prime Numbers as 1,4,6,8,9
Each group of pipes has passed through every row, column, and box in that room, And the pipes in the same group must be fully connected into a complete network. But just now, someone accidentally touched the valve in the network, and the numbers basically flowed away, left behind these empty pipes. There is no time left, could you please act as a plumber to fill the numbers to repair the network in this room?
P.S. This network is composed of three overlapping groups, and different groups can cross each other. All numbers belonging to a certain group must be in the pipeline of that group.
CTC link. Have fun solving!
Solution code: The Group 1 of column 5, then Group 2, Group 3. 15 digits no space. For example: 987654321→975319876598641
Comments
on 10. October 2023, 00:27 by sanabas
Does every instance of orthogonally connected digits from the same group need to have a direct connection? e.g. r8c9 is a 3, can r7c9 be a 5?
Does every instance of a connection between two cells have to have a group 'flowing' through it? e.g. r4c7 is 8, can r4c8 be 5, and the bit of pipe connecting the two cells is unused?
I gived all orthogonally connected， so there must has a line between two same group of digits, and if there has no line, two digits must not be in the same group.
on 8. October 2023, 20:36 by Chami
I'm not sure if I understood the rules correctly. Maybe you could help me:
1. Do standard Sudoku rules apply?
2. Since there are only 5 “Ends”: Is one endpoint occupied by 2 Groups? Or is one pipe-end just not visible? Or do the “ends” not matter at all?
3. Similar to question 2: Can the pipes run alongside each other or can they only cross over? E.g.: Can R4C3 be in two groups at the same time?
Q1: Yes，it does.
Q2: The “ends” not matter at all. There are branches in every group of the pipeline.
Q3: One digit can be in two different groups, even three, such as "9", it should be in three groups at same time. And that's where the two different groups of pipelines crossed.
Hope these can help you.
