A Sudoku solution with set based T-SQL utilizing binary operators.

The table numBinaryDigits is an auxiliary table that stores all possible values (1~9) and their corresponding binary values in this solution.

The UDF udfConvertBinaryToDecimalString converts a binary value to the comma delimited decimal list, just to help the output.

In the stored procedure uspSolveSudoku:

1. There are three elimination rules, as listed below. The first rule will be considered as first method, the last two will be considered as second method. Each time after a second method is applied, the first method will be applied until no newly determined cells found.
   • Rule 1: Eliminate determined values from un-determined cells in the same range
   • Rule 2: Determine the cell that solely contains a possible value in the same range
   • Rule 3: If two cells in the same range have and only have the same pair of possible values, eliminate the pair of values from other cells in the same range
2. The first parameter @T should be the original puzzle in string format of 81 characters in length, 0 for empty cells
3. The second parameter @Trace is a flag to ease the trace of code execution, showing how many times any of second elimination methods have been executed and the overall execution time. If the flag is on, the second elimination method queries will also be printed in the message pane.
4. Dynamic queries are used just to make the logic more readable, and could be replaced by static queries, which will increase the performance by 30-40% based on my test.
5. In the dynamic queries, the "Range" refers to a row, a column or a block which will be replaced by "r", "c" or "b" just before execution.
6. You might want to add "goto OutputSudoku" at the place where you want to stop the execution to see the interim result.

You might also want to play around with this solution by switching to table variable or physical table instead of using temporary table (#s). For using table variable, you have to make the table visible to the dynamic queries or change to using static queries. For using physical table, you can also try to use a persisted computed column instead of column "d". In this case, you need to create a function WITH SCHEMABINDING that gives the number of possible values for the v column value in the same row, the same result as "select count(*) from numBinaryDigits where (v & vBinary)>0". This could also increase the performance a bit, but not too much.