John and Bettan are friends with Noah. They wanted to know when Noah's birthday is, Noah gives list of *10 possibilities*:

\(\text{May 15} \quad\quad\quad\text{ May 16} \quad\quad\quad\text{ May 19}\\ \text{June 17} \quad\quad\quad\text{ June 18} \\ \text{July 14} \quad\quad\quad\text{ July 16} \\ \text{August 14}\quad\quad\quad\text{ August 15}\quad\quad\quad\text{ August 17}\)

Noah tells his birthday's day and month respectively to Bettan and John.

\(\text{John : I don't know when's Noah birthday, sure John doesn't knew too} \\ \text{Bettan : At first I too don't know, but I now know his birthday} \\ \text{John : I too knew Noah's birthday}\)

**So, when is Noah's birthday?**

** If you got the answer, post a solution how. Just don't guess, apply a lot of logic**

*This problem has been asked by a 14 year old student!*

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