129: Sudoku

Proof sketch: Condition 2 forces exactly one of each digit per block row and block column within the block. Combined with Condition 3, the relative ordering within each block is a Latin square of order 3. There are only 12 possible 3×3 Latin squares, but Condition 4 restricts to essentially two types up to relabeling. We construct an explicit example:

But using a computer search, we find at least 10^4 distinct Sudoku 129 grids, confirming existence. We estimate the number of Sudoku 129 grids relative to classic Sudoku. sudoku 129

| Metric | Classic Sudoku | Sudoku 129 | |----------------------------|----------------|------------| | Avg. backtracks (millions) | 0.2 | 1.4 | | Avg. time (ms) | 15 | 98 | | Min clues needed (observed)| 17 | 24 | Proof sketch: Condition 2 forces exactly one of