I’m solving a numeric crosswords (something like this), and I run into an odd issue. I’m using integer programming and Cbc solver. If I type in all the constraints resulting from the given clues (sums of digits in all given groups), I receive following error:
WARNING: Not solved to optimality, status: Infeasible
WARNING: Infeasibility ray (Farkas proof) not available
WARNING: Variable value not defined for x. Check that the model was properly solved.
If I remove a few clues randomly, then the problem gets solved correctly. Some clues are more sensitive than others. I found a single clue, which can be omitted and solution is found. If I add that specific clue, I need to remove about 5 other clues in order to don’t have the above quoted error. All the clues are perfectly valid and not contradicting themselves. Even typing a few obvious hints, like “put 4 in this cell”, which theoretically should simplify the problem, causes above error.
Question: what exactly the error means and how can I get better insight into what is actually wrong? Or is it Cbc bug?