The Omnifarium - Sudoku/49.html

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I am no longer posting new puzzles to this blog. For all of my Sudoku puzzles, old and new, please visit Sudoku in another section of this website. I will still create and offer new puzzles, in batches of a couple of hundred, once a week or so.

Sudoku #49

Category: Sudoku
Fri, 12 Aug 2005, 07:05

Look carefully at todays puzzle and you might find something a bit unusual. Can't see it? Then before reading any further, start solving it.

Did you figure out yet what's unusual? Look for the number nine in the start values. I got curious, and changed my Sudoku program to generate puzzles without certain given start values. As I suspected, it is possible to have valid puzzles without all digits from one to nine represented in the starting grid.

Is there a minimum number of start values needed for a valid puzzle? I suspect you need eight or nine specific starting values. Consider a puzzle that starts with the seven values from one to seven. As you're solving the puzzle, you'll reach a point where you have some number of unknown cells with the possibilities {8,9}, with nothing further to go on. To have a solvable puzzle, at least one of those cells would have to have either an eight or a nine initially.

As a further test, I told my program to generate a puzzle with two values missing, and it couldn't do it. Mind you, I only gave it a few hours. But that's enough time to generate a couple of thousand puzzles otherwise.

Hans

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