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?