Like most interesting games, when turning them around by redefining what loses is now what wins, a fascinating variant can be played. For example, in Chess, if the object is to now be the first player to lose all pieces except the king, and a capture is forced if it is available to be played, this yeilds a variant, called Losing Chess that even novice players can excel at.
Another game is called Losing Checkers where you play Checkers according to normal rules (forced to capture if the opportunity arises) but the Loser wins.
In this spirit, I thaought about what it might mean for Sudoku puzzle solving. Since there are so many ways you can fail to solve a puzzle, this didn’t seem to challenging 🙂
In this Cartoon variant, We start with a Sudoku solved puzzle and proceed to erase numbers until we have an incomplete or starting puzzle (depending on when you stop erasing). Then try to solve the puzzle that is presented.
If you don’t erase enough numbers, the puzzle may be easily solved. If you erase just enough numbers, (in this case 53 of them), you may either have a uniquely solvable puzzle with a single solution or you may have one with more than one solution. If you keep removing more than 53 numbers (in this case), your ultimate solution may have multiple answers. This means that your starting numbers are “ambiguous”.
There are many programmatic aids in solving sudoku puzzles on the internet, both web based and downloadable applications. One category are Sudoku Puzzle Generators where they produce the starting numbers and you solve. There are also Sudoku Solver Sites, many of which have user interfaces so that *their* puzzle may be solved by you online.
The trick is to find Sudoku Solvers where you get to input the starting numbers. Some sites I found offer:
(1) Excel based Sudoku all in one Generator and Solver by Hari Kumar
(2) Excel based Sudoku-xls Generator, Workpad and Solver by Peter Mladek
(3) AT&T Research Command line: A 9 x 9 Sudoku Solver And Generator And Starting Number analysis
(5) David Ireland’s Number Sudoku Solver (Excel Based)