I think it's a paradox, and doesn't have a proper solution.
But we can try like this :
the hanging can't happen on Saturday, because it's the last possible day, and it wouldn't be a surprise
It can't happen on Friday, because it's the last day when it's not the last day, and equally wouldn't be a surprised.
It can happen on Thursday, because it's neither the last possible day nor the last day when the hanging can happen; but it won't in reality because it's last such day, no similar day is after it. so in a way it's special too
Wednesday, however, leaves more than 2 days after itself (just like Thursday), but it's not the last day with this characteristics. On Wednesday morning Wed and Thurs are equally possible. On thurs however only thurs is possible, as Wed has passed already.
( I am not sure about this, but that's how I understand it)
