28.02.2025, 19:57
(Dieser Beitrag wurde zuletzt bearbeitet: 28.02.2025, 20:39 von Screature.
Bearbeitungsgrund: Added minimal set reasoning, added attachment and rules
)
I've answered my own question! I created one in the attachment with the rules boiled down to:
1) In each 5x5 square, each row and column must contain digits 1 to 5.
2) If you were to map all instances of a single digit from one square onto the other squares, the maps must also contain digits 1 to 5.
3) Each square cannot be solved individually in isolation without context from the others.
https://imgur.com/a/qIMqH2a
This shows the solving steps of a 5x5 MOLSudoku. I'm giving it that name coz I can't find any similar puzzles online. Yeah there may be similar puzzles at depth 2 but I took it to depth 4 and reduced to a set of 32 clues, where each individual square cannot be solved independently of the others. In this series of images:
Step 1: Start with the empty puzzle.
Step 2: Fill in as many singles and candidates as you can (rows and columns in each 5x5 must contain digits 1 to 5).
Step 3: Notice that all the 3s are filled in top left, so map them to the others.
Step 4: The maps on the others have to contain digits 1 to 5, so fill in those digits.
Step 5: Disregarding the top half for a moment, the left can be filled in but the right still has multiple solutions.
Step 6: Highlight the 1s on the left, arbitrarily, and map onto the right.
Step 7: Fill in those digits as the map has to contain digits 1 to 5.
Step 8: This square can now be completed.
Step 9: Considering the top half again, the right can be fully completed but the left is still ambiguous.
Step 10: Highlight the 2s on the right, arbitrarily, and map onto the left.
Step 11: Fill in those digits as the map has to contain digits 1 to 5.
Step 12: Complete the rest of the puzzle!
Also the generator I made (with the help of Claude, yes, I'm not an expert by far), can reduce the puzzle down to a critical set of just 4 clues per square, 16 in total, still with one unique solution. I couldn't figure out the multiple layers of logic needed to add many digits so I found those way, way too difficult. I could be proven wrong by a top puzzle solver, but for now I'll stick with 32 total clues.
1) In each 5x5 square, each row and column must contain digits 1 to 5.
2) If you were to map all instances of a single digit from one square onto the other squares, the maps must also contain digits 1 to 5.
3) Each square cannot be solved individually in isolation without context from the others.
https://imgur.com/a/qIMqH2a
This shows the solving steps of a 5x5 MOLSudoku. I'm giving it that name coz I can't find any similar puzzles online. Yeah there may be similar puzzles at depth 2 but I took it to depth 4 and reduced to a set of 32 clues, where each individual square cannot be solved independently of the others. In this series of images:
Step 1: Start with the empty puzzle.
Step 2: Fill in as many singles and candidates as you can (rows and columns in each 5x5 must contain digits 1 to 5).
Step 3: Notice that all the 3s are filled in top left, so map them to the others.
Step 4: The maps on the others have to contain digits 1 to 5, so fill in those digits.
Step 5: Disregarding the top half for a moment, the left can be filled in but the right still has multiple solutions.
Step 6: Highlight the 1s on the left, arbitrarily, and map onto the right.
Step 7: Fill in those digits as the map has to contain digits 1 to 5.
Step 8: This square can now be completed.
Step 9: Considering the top half again, the right can be fully completed but the left is still ambiguous.
Step 10: Highlight the 2s on the right, arbitrarily, and map onto the left.
Step 11: Fill in those digits as the map has to contain digits 1 to 5.
Step 12: Complete the rest of the puzzle!
Also the generator I made (with the help of Claude, yes, I'm not an expert by far), can reduce the puzzle down to a critical set of just 4 clues per square, 16 in total, still with one unique solution. I couldn't figure out the multiple layers of logic needed to add many digits so I found those way, way too difficult. I could be proven wrong by a top puzzle solver, but for now I'll stick with 32 total clues.
