I don't know where else to ask this, but I don't really understand one part in the famous eye color island question/puzzle. Here is an example of the question/puzzle on mathematics stack exchange:
This puzzle is obviously not mine and is famous, including being on Wikipedia.
In the correct answer, I have a problem with this statement about the case where there are two blue-eyed islanders:
After no one leaves on the first day, each blue eyed person can correctly deduce that the other blue eyed person must have seen someone with blue eyes, and it must be themselves.
How can the blue eyed person deduce that the other blue eyed person saw themselves as blue eyed? What if a brown eyed person deduced that?
One way I can see how the blue eyed person could deduce they must have blue eyes if no one left on the first day was if they knew the number of brown eyed people on the island. Then they could deduce there must have been someone else with blue eyes. But if they knew the number of brown eyed people, and they knew the number of people, then they would know the number of blue eyed people, which would be extra information (knowing the number of blue eyed people on the island) inconsistent with the original puzzle.
Can anyone explain it to me in simple English terms?