Quiz - The monks

[kam]

There is one monastery with 7 monks. They are not speaking either making any signs with hands. They just pray every day all together in the morning around a round table. This is the only time every day that they can see each other. Remember. They just look each other with NO OTHER WAY of communication.

One day, a man appears to the monastery. He tells to each monk separately the same story:
"All monks have a sign on their forehead, so do you. Some of you have the sign of satan, a red dot, and some of you the sign of god, a red cross. Those with the sign of satan must leave the monastery"
He told only this to each one and then left. NOTHING more.

In a few days 3 monks left the monastery. They had indeed the sign of satan. All other monks had the sign of god.

1) How did these monks found out that they had the sign of satan?
2) How many days they took to find it out?

* No mirrors or other reflecting/projecting devices exists
** we assume that all monks think the same way
*** The answer is clever, do not reply like "they had vision", or "they paid the man to tell" or "they saw it on the reflecting water in the sink". No.

[kam]

no one with an answer?

[tpone]

Every day 2 monks where siting one in front of the other. If the monk had a mark, then the other was rising from the chair. So in 6 days where found 3 monks with the sign and they left.

eh?

[kam]

no not really

[Stefano]

Can they do something like standing up or sitting?

[kam]

nope nope nope


All right. They can only:
1-Look
2-Think
3-Go away of the monastery and not come back

Ok?

[kam]

Oh and of course, every morning they gather in a round table to pray. There they can look each other but only this.,

[Erkeli]

The monks that left where 3!
- solution -
They must thing the same way as you said.

if 2 monks had the satan sign. The first day, everyone was looking each other. The "clean" monks could see 2 monks with the sign and each one of the "satan" monks could see another 1 satan monk. But day 1 no one would leave as everyone could see another satan monk. Day 2, because no one would have left, the satan monks that could see only 1 more satan monk would understand that because this monk did not leave, there is another one with the satan sign and because they could see only 1, this means that they had also the satan sign. So, in day 2, 2 monks would leave.

Now that the monks are 3 (you will see why) the satan monks sees 2 more satan monks. In day 2, they would expect these 2 satan monks to leave (as per previous lines). In day 3 that they see no one leaves, they would understand that there is one more that these 2 satan monks can see with the sign and so, because they could see only 2 satan monks they understand that they had the sign. In day 3, 3 monks left.

e?

[kam]

CONGRATULATIONS
If you found it by your self, congratulations!
This is almost the answer. It is absolutely correct i just know it in another way.

[Supernova]

nice and clever!

[manley_V]

Erkeli, it took me an hour to understand your answer. And still is not very clear. You found it by yourself or you knew it? It's very nice!

[tpone]

Nice after all