Saransh's birthday

There were three friends Saransh, Ameya and Mayank and they have joined the college VIT recently so they were sitting outside p-block (a building name) and talking about their past life and birthdays and Ameya told about one of the incident that happened a few days ago when he was in his home town Amravati. He told that they had a party on the occasion of the birthday of one of his friends and after the party they beat him and had fun. Now in order to celebrate a birthday as early as possible both Ameya and Mayank were excited to disclose their birth date to each other but Saransh being afraid of beating agreed to give only partial information about his birth date. He gave a list of dates out of which one was his birth date, here is the list :

He then told Ameya the correct date of his birth date and Mayank the correct month of his birth date. He discloses this information on the condition that Ameya and Mayank will not reveal the month and date to each others and then he left for a walk. Mayank and Ameya keep wondering how to get the exact birth date of Saransh without diclosing their respective information and they had a conversation:

Mayank : I don't know the date but I also know that you don't know either.

Ameya : You know what Mayank, you were right at first I didn't know but now I know.

Mayank : Oh man! Now, I know it too.

Now, the problem for you is to analyse the conversation and deduce the birth date of Saransh.

To solve this problem let us construct a table where columns represent the dates and rows represent the months

Now we have to use a liitle bit of brain here and apply some logic. If we see the conversation at first Mayank told Ameya that I don't know the date but I know you don't know either, so now we start thinking about what Mayank said, we can deduce that if the month that Mayank knows was either May or June then he would have known that Ameya know the exact date Why? because there is only one possible date for May and June thus the month that Mayank knows has to be either July or August.

Now we eliminate those months from the table and the table looks like :

Now, we can conlcude one more thing that the day is not 8th for sure Why? because If that would be the case Ameya should have said still don't know or something like that but instead he said At first I didn't know but now I know, so the date has to be 9th, 10th or 11th otherwise it would be ambiguous for Ameya to know the birth date, hence the table now reduces to :

Now, if we look at what Mayank replied, he said that, now he knows too so we can say that the month is not August because if it would have been so he would have said that still don't know or something like that but he is certain that he knows that's why the the month has to be July otherwise it would be ambiguous for Mayank to know the birth date.

So the table has only one entry now:

Hence we can conclude on the basis of this strange conversation that the birth date of Saransh is 10th of July!

God save him.

The original problem was named as Cheryl's birthday which went viral in 2015. I just modified the dates so that it matches with my birth date. Here is the original one :

Hope you enjoyed the article, have a nice day!