Question

Brain Challenge or Brain Challenge:
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Radha is the new child of Ramu and Raju. One day, they both asked Radha for her birthday. After consulting one, Radha said, I'm not going to say, but give you a clue. Radha then handed them a list of 10 dates and said, "My birthday is one of these dates".

July 13th, July 17th

May 16, May 17, and May 20

June 18 and June 19

Aug. 13, Aug. 16, Aug. 18

Then she told Ramu's ear only the month of her birthday. Likewise, Raju's ears were told only on the day of birth. Then he asked Ramu "Did you get the grip?"

Ramu: "I don't know, but I'm sure Raju doesn't know either."
Raju: "I didn't know until Ramu said this, but now I know."
Ramu: "Now I got it"

Q: What date is Radha's birthday given above?

PS: 1. This is not a cunning question. It is a clear-cut question that needs to be solved logically. If someone answers their own brain talk, let's discuss.
Any one can answer the Q .. ???​

Answer 1

The given 10 dates are mentioned in the following table:

$\begin{tabular}{|c|c|c|c|c|c|c|} \cline{1-7}May && 16 & 17 & && 20\\ \cline{1-7}June &&&&18&19&\\ \cline{1-7}July & 13&&17&&&\\ \cline{1-7}August & 13&16&&18&&\\ \cline{1-7} \end{tabular}$

Now let us come to the conversation between Ramu and Raju.

1. Ramu: I don't know, but I'm sure Raju doesn't know either.

• >> Ramu cannot find the birthday because all he was told, was the month. However Ramu could figure out the date being one of May 20 and June 19, as they appear only once in the list (if he was told any one of the days 19 or 20).

$\begin{tabular}{|c|c|c|c|c|c|c|} \cline{1-7}May && 16 & 17 & && \boxed{20}\\ \cline{1-7}June &&&&18&\boxed{19}&\\ \cline{1-7}July & 13&&17&&&\\ \cline{1-7}August & 13&16&&18&&\\ \cline{1-7} \end{tabular}$

2. Raju: I didn't know until Ramu said this, but now I know.

• >> The only way that Raju can know is if his months are July and August, since then only he can exclude Ramu's months being May and June.
• $\begin{tabular}{|c|c|c|c|c|} \cline{1-5}July & 13&&17&\\ \cline{1-5}August & 13&16&&18\\ \cline{1-5} \end{tabular}$
• >> From Ramu's deduction, it is clear that the possible days are 13, 16, 17 or 18. But for him 13 appears in both July and August. So he has to take 16, 17 or 18 as the most possible days.
• $\begin{tabular}{|c|c|c|c|} \cline{1-4} July & & 17 & \\ \cline{1-4} August & 16 & & 18 \\ \cline{1-4}\end{tabular}$

3. Ramu: Now I got it.

• $\begin{tabular}{|c|c|c|c|} \cline{1-4} July & & \boxed{17} & \\ \cline{1-4} August & 16 & & 18 \\ \cline{1-4}\end{tabular}$
• >> The only days left are July 17 and 16, 18 of August. But none can figure out the exact date if it was of August's.
• >> The correctt answer is therefore July 17.

< Radha's birthday is on July 17. >

Riddle questions:

Q1. Someone’s mother has four sons. North, South and East. What is the name of the fourth son. 

https://brainly.in/question/16223198

Q2. These all are different from each other. They are all unique in themselves. Find the correct answer from the given picture.

https://brainly.in/question/4063870

Q3. What is seen in the middle of March and April that can’t be seen at the beginning or end of either month?

https://brainly.in/question/9096119

Answer 2

July 17 is Radha's birthday.

Step-by-step explanation:

The choice of dates are:

July 13th, July 17th

May 16, May 17, and May 20

June 18 and June 19

Aug. 13, Aug. 16, Aug. 18

We first eliminate unique dates because that would have made Raju and Ramu guess easily. So June 19 and May 20 is removed. This helps us to further eliminate the months containing these two dates which brings us to remove May and June dates. We are now left with either July (2 days) or August (3 days).

Now we have to eliminate the common date between July and August, which makes us remove July 13 and August 13.

We are now left with July 17,  and two dates in August.

The date has to be unique for Raju to guess. So August will be eliminated as it has two dates which will make it difficult for Raju to guess.

So the only unique date we are left with is July 17.

Hence July 17 is Radha's birthday.