You are Pat Doe, a lowly Sudoku puzzle-maker eking out a living by producing hand-made Sudoku puzzles.
After an exhausting eight hours, you've just completed your last Sudoku grid for the day. Unfortunately, it's only after you've completed the grid that you realize the usual $3\times 3$ blocks aren't legal (none of them contain exactly the digits 1 thru 9). To make matters worse, your hand malfunctioned and inserted several bold lines denoting boundaries of neighbouring blocks in unusual places.
Rather than redoing the entire grid, you resolve that you will find out a way to partition the grid into 9 irregular blocks (nonominoes) in such a way that:
- each block contains the digits 1 thru 9 each exactly once
- the blocks respect the existing boundaries (i.e. a boundary may appear nowhere on a block except at its borders)
Can you recover from your error? Can you partition the grid and salvage a workable (if highly irregular) Sudoku grid?
Good luck! :)
The following is an example of a valid block. It is a nonomino containing the digits 1-9 each exactly once, and it respects established boundaries.
The following is not a valid block because it is not a nonomino.
The following is not a valid block because it doesn't respect existing boundaries.
Answer
My solution:
Solution method:
I didn't do anything that systematic or logical. I made some vague approximate clusters that had most of the digits 1-9. Then, when a cluster needed a number that it wasn't adjacent to, I'd have it "trade" numbers with adjacent clusters. Often, a whole chain of trades was needed. Though I started on the right and went left, fixing a single disconnected cell in the last incomplete cluster caused a chain reaction that made me reconstruct the bottom right section of the board.
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