Guessing Birthdays
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Sarah and Derek are students of Mr Tan. Mr Tan’s date of birth is on N/M/1970 and both of them know that Mr Tan’s birthday is one of these 10 dates:

4/3/1970, 5/3/1970, 8/3/1970, 4/6/1970, 7/6/1970, 1/9/1970, 5/9/1970, 1/12/1970, 2/12/1970, 8/12/1970

Mr Tan tells Sarah the value of M and tells Derek the value of N. Then Mr Tan asks them: “Do you know when my birthday is?”

Sarah says: “I don’t know, but I can be sure that Derek doesn’t know either.”

Derek says: “Initially I don’t know, but now I do.”

Sarah says: “Oh, then now I know it too.”

Based on this dialogue and the dates given, can you figure out which is the correct date of Mr Tan’s birthday?

(write it as it is listed above)