Quite enjoyed tackling the following question, that I sourced from Skorks.
There is a village full of people. One day the priest gathers all the villagers together and declares that their God has told him that some among the villagers are sinners. All sinners will be marked with a sign on their forehead so that all other people will be able to see if a person is a sinner or not, but noone will know if there is a mark on their own forehead. Furthermore, the mark will not be visible in the mirror and one person is forbidden from telling another if they are a sinner. The villagers must work out which among them are sinners at which point all sinners are to leave the village. The village has been given one week and if at the end of the week, there are still sinners present, the whole village will be destroyed. The villagers go about their own business during the day, however the whole village gathers in the square at the end of every day so that everyone can see if there are still any sinners left among them. After the third such gathering all the sinners pack up their stuff and leave the village. How many sinners were there?
