Example of Splits
This is a version 14.0 screenshot
Splits:
If all the other Analyses have failed to find a complete Solution, then the Splits Analysis may be deployed. Whether you consider this approach 'logical trial-and-error', or just 'guessing', the procedure is the same:For each Square which contains a Pair (coloured pink), one Possible of the Pair is trialed. If it leads to a Contradiction, then the other Possible of the Pair must be the true Solution. If no Contradiction is forthcoming, the Analysis trials (or 'guesses') the next Pair and so on until a complete Solution is obtained.
Because the Analysis does not check both values of the Pair for Contradictions (unlike the Impossible Solutions Analysis), any Solution that is reached may not be unique - it is possible that either value of a Pair may lead to a Solution, meaning the SuDoku is not a true puzzle with a unique Solution.
Second Example of Splits
This is a version 14.0 screenshot
In this second example, an additional Start Position Square has been added which allows the other Analyses to progress much further, but the last few Squares still cannot be solved and the Splits Analysis kicks in. This indicates the SuDoku does not have a unique Solution - the 5s and 8s are interchangeable between the two possible complete Solutions.
If the Splits Analysis can find a Solution, but the Impossible Solutions Analysis cannot, this is a pretty strong indication that the SuDoku does not have a unique Solution.
If the Splits Analysis can find a Solution, but the Impossible Solutions Analysis cannot, this is a pretty strong indication that the SuDoku does not have a unique Solution.