Friday Puzzle #133 - Low-clue Killer Sudoku
A lot of recent sudoku news has focused on the reported proof of 17 being the minimal number of clues needed to specify a unique classic sudoku solution. I haven't had time to look too deeply into the proof yet but at first read it seems to be one of the better pieces of sudoku scholarship to come out since the full counting of solutions done by Jarvis and colleagues many years ago. It also led to a lot of mail in my inbox asking if I'd seen it (every single email following my first observation, telling me I am still more on the pulse of sudoku than most everyone else) and, as usual, a small majority of these emails were talking about some proof in sudoko instead.
Anyway, one of those messages came with a fun 16-clue Killer sudoku. I figured the actual minimum in what some call the "Zero Killer" style should be much lower, but I'd never tried to push that extreme very hard myself so I put together this 12-clue symmetric cage puzzle by hand in a little bit of time. I'm guessing 11 cages is possible but lower might be too, certainly if asymmetry is allowed, within my rules of no repeats in cages, no cage overlap, and only edge adjacent cells in cages. Certainly when you allow diagonal adjacency and crossing you can turn up a 10-clue zero killer or a 13-clue "regular" killer when all cells must be in a cage (HATMAN is the source for both of the linked puzzles). I personally dislike the diagonal adjacency with crossing as the sense of "what belongs where" is nowhere near as clean until you color the cages, but perhaps Killer definitions are too far across the board for a meaningful minimum definition in the community anyway. Still, I thought this example puzzle was a pretty good solve, so I'm sharing it this week.
Rules: Insert a digit from 1 to 9 into each cell so that no digit repeats in any row, column, or 3x3 region. Additionally, some cages are drawn in the grid. The number given as a clue in each cage equals the sum of the digits in the cage, and digits cannot repeat in any cages.
Solution
Anyway, one of those messages came with a fun 16-clue Killer sudoku. I figured the actual minimum in what some call the "Zero Killer" style should be much lower, but I'd never tried to push that extreme very hard myself so I put together this 12-clue symmetric cage puzzle by hand in a little bit of time. I'm guessing 11 cages is possible but lower might be too, certainly if asymmetry is allowed, within my rules of no repeats in cages, no cage overlap, and only edge adjacent cells in cages. Certainly when you allow diagonal adjacency and crossing you can turn up a 10-clue zero killer or a 13-clue "regular" killer when all cells must be in a cage (HATMAN is the source for both of the linked puzzles). I personally dislike the diagonal adjacency with crossing as the sense of "what belongs where" is nowhere near as clean until you color the cages, but perhaps Killer definitions are too far across the board for a meaningful minimum definition in the community anyway. Still, I thought this example puzzle was a pretty good solve, so I'm sharing it this week.
Rules: Insert a digit from 1 to 9 into each cell so that no digit repeats in any row, column, or 3x3 region. Additionally, some cages are drawn in the grid. The number given as a clue in each cage equals the sum of the digits in the cage, and digits cannot repeat in any cages.
Solution
