Example of Impossible Solutions
This is a version 14.0 screenshot
Impossible Solutions:
Like the Splits Analysis, Impossible Solutions starts off by identifying a Square with just two possibles. But unlike Splits, it will only proceed if it finds a Contradiction when trialling the possibles.In this example, the first Square with a Pair, one of whose possibles causes a Contradiction, is A5 with possibles 4 and 5. When trialling the 4, it ultimately leads to a Contradiction on B9, which means the 4 on A5 is impossible and may be eliminated.
The path from trialling a 4 on A5 to causing a Contradiction on B9 may take many steps and these may be viewed by clicking the TRACE button. Alternatively, just click the STEP button as usual to remove the 4 and allow the Solver to proceed.
Example of a Impossible Solutions
This is a version 14.0 screenshot
Impossible Solutions:
In this second screenshot, the Trace button has been clicked which brings up a dialog box on the right-hand side. This shows that the first step in the trace identifies Uniques on A6, A7, J5 and J6. Within the dialog box, clicking STEP will continue to step through the trace until the Contradiction is reached; or clicking CANCEL will end the tracing exercise.Example of Impossible Solutions
This is a version 14.0 screenshot
Impossible Solutions:
In this third screenshot, the STEP button within the dialog box has been clicked 6 more times to advance the trace through 6 more Analyses steps, which ultimately leads to all the possibles on B9 being eliminated, which is the Contradiction.In Summary, if the Impossible Solutions Analysis leads to a Solution, that Solution is guaranteed to be Unique. If the Impossible Solutions cannot find a Solution, but the Splits Analysis can, the SuDoku probably has multiple Solutions and isn't a true puzzle.