The logic actually does work. When you've gotten to the point where you can prove that it won't be Friday and then remove it from the set you are left with Monday through Thursday as possibilities. This means that we know, logically, that Friday could not possibly be the day of hanging. We can remove it from the set. We never add it back into the set, because the moment that Friday is an option, it becomes the last day in the set and therefore we know that the hanging cannot happen on that day. Because, as we've shown, the hanging cannot happen on the last day. This means that if we look at Monday-Thursday as our set, the hanging cannot happen on Thursday because it is the last day. On Wednesday afternoon, we know for certain that he will not be hanged on Friday (because if he were it would never be a surprise) and therefore know for certain that he will not be hanged on Thursday because it is the only other option and so it will not be a surprise. In other words, because Friday could NEVER be a surprise, Thursday cannot be a surprise. Even though there are two days left. On Tuesday afternoon, we know that the hanging could never happen on Friday, and therefore could never happen on Thursday. If that's the case, then it could never happen on Wednesday, either. The reason is that surprise is connected to uncertainty. If there are two options for when it could happen then there's is uncertainty. The stated problem gives the illusion of options when there are none. On Wednesday afternoon there is the illusion of two options (two days) but we know with certainty that it would not happen on Friday and therefore we have only one option, which means no uncertainty and therefore no surprise.