In Faraway Land there is a monastery built atop a mountain in which monks live isolated from the rest of the world.
The monastery is made of two large buildings: one is where the monks sleep, the other is where they all spend the days together, working or minding their own business.
In this monastery, there is a rule that forbids the monks to communicate with each other, whether it's through writing, talking, or body language, they are not allowed to communicate at all.
One day, the master of the monastery decides to exceptionally break that rule to inform his fellow monks of one important fact:
There is an illness among us. It is fortunately not contagious nor particularly dangerous, but I would like every single one of you to remain in bed for an entire day once you know you have contracted it. The illness has only one recognizable symptom: it causes an easily visible red dot to appear on one's forehead.
Unfortunately, there are no mirrors in the monastery and nothing else that might help the monks see for themselves if they have contracted the disease or not. Fortunately, every single monk is highly intelligent and wouldn't require any help in the first place.
Seven days pass without a single monk missing. After the seventh day (on the eight day), all sick monks suddenly remain in bed resting just as the master had instructed them to. How many monks were ill and how did they find out?
You may assume the following:
- How many monks live in the monastery is irrelevant to the puzzle.
- All of the sick monks were already sick and had visible symptoms when the master made his announcement, no other monk fell sick since then.
- None of the monks had visible symptoms the day before the master made his announcement.
- "The first day" is the day the announcement was made. "After one day" means the first day has passed and it is now the second day.
- There was at least one sick monk.
- The master is to be considered a monk like every other.
- Whether the master was among the sick monks is irrelevant.
- The master broke the rule to make his announcement only, nothing else.
- The monks do not communicate, but they see every other monk every single day, therefore they know exactly who was missing and who wasn't, as well as who was ill and who wasn't.
- The monks never forget. Ever.
- Only the sick monks stayed in bed on the eight day and nobody else.
- There is no third party involved in this puzzle, the monastery is completely isolated from the outside world.
- No monk tried to leave and no new monk arrived to the monastery during those seven days.
- The monks' solution is the best solution given their circumstances.