Logicians A and B ask lady C her age.
Lady C gives 11 different numbers one of which is her age to logicians A and B:
35, 36, 38, 42, 45, 46, 51, 55, 57, 61, 62
Then lady C tells the digit in tens to logician A and tells the digit in ones to logician B.
Logician A says: "I don't know the age of lady C. I think/know logician B does not know either."
Logician B says: "Initially I don't know the age of lady C, but now I know."
Logician A says: "Oh. Then now I know too."
Question: What is the age of lady C?