See also: Entrance examination for the Ecole Polytechnique (France): First math test (1986). One question at the end remains unsolved... (even though it can be bypassed to solve the problem)!!
15/04/2015: I have just discovered recently that this enigma (that I just reproduced from memory) is apparently due to the French mathematician Jules Henri Poincaré (but actually I do not have the exact original version). The statement given here is therefore just an adaptation of the original enigma (in which it was specified that the monks are bouddhist monks).
40 monks live together in a monastery. They have very strict rules which are followed by all of the monks at all times. One of the rules is, that absolutely no communication between monks is allowed. Another is, that mirrors are forbidden. The monks have their three meals a day together in a large hall, the rest of their day is spent with individual contemplation and chores. The morning, the Father Superior, who is the only one authorized to speak, gives information for the day to the other monks.
One day, the Father Superior give them some very bad news. A dangerous disease appeared recently in the country, and finally came to the monastery. The single symptom of it (before death..) is the existence of a red spot on the forehead, but it is not contagious (at least before death occurs).
In order to avoid this disease to spread in the monastery, the Father Superior tells the monks that any monk knowing he catched the disease must leave the monastery. But no one leave the monastery after his speech.
The next day, the Father Superior tells again the monks that any monk knowing he catched the disease must leave the monastery. But no one leave the monastery after his speech.
The next day, the Father Superior tells again the monks that any monk knowing he catched the disease must leave the monastery. After he finished, all the monks that were sick leaved the monastery.
How many monks were sick?