>>>>Since, according to the premise, the mayor should know about at least 39 of the 40 unfaithful wives - and the other townsmen know that he knows - he will get into trouble for his understatement.
>>>
>>>Well, there is the taboo. It doesn't say that they can't say anything. Maybe the mayor decides to take unilateral action and be diplomatic about things at the same time.
>>>
>>>Unless his wife is also unfaithful, he should know exactly how many women will be shot and when.
>>
>>I don't understand why anyone will be shot, if the mayor said something which everybody knew anyway. What new information is he giving?
>
>Allright say there is 1 unfaithful wife.
>What will happen?
>
>Remember the man knows about every unfaithful wife except his own.
>And because of the taboo, noone would have told him anything until now.
>
>Remember, you can clean from what the Mayor said that there must be at least 1 unfaithful wife.

If there would be just one unfaithful wife, then the result is very clear - she would be shot immediatelly.

But the Mayor didn't give any new information - all of men already knew that there are either 39 or 40 wives, that unfaithful. I could not find a connection to the solution, though I feel it is a combinatory (what's the English word?) type of problem.