Question

Vikram and Muthu befriended a girl. Asks her what is her birthday. She does not give a straight forward answer, but some hints
She gives them the following 10 dates to pick the right one from
May: 15, 16, 19
June: 17, 18
July: 14, 16
August: 14, 15, 17
She disclosed correct month to Vikram alone and correct date to Muthu.
Asks Vikram to guess the right birthday. He says sorry I can't, but I am sure even Muthu won't be able to guess it right.
Now Muthu says, I was a bit confused but with Vikram's statement, I know what is her birthday.
Now Vikram says if that is the case, I also know what is it.
Both guessed it right. Use simple logic to guess the right birthday. Go ahead

Answer 1

The answer to this question is July 16.

• Muttu is told the date. The dates are surely not 18 or 19. Since these dates appear only once and it would become easy to directly guess the birthday.
• Vikram is told the month. But he is sure even Muttu cannot guess the date. This indicates that the month is surely not May or June because they have the dates 18 and 19. If Vikram is sure Muttu cannot guess the month, the unique dates (that appear once) cannot be in the month.
• We are left with July and August and dates 14,15,16,17.
• Muthu was able to guess the date now. So it has to be a date not repeated in July and August. Hence, date is not 14.
• We are left with July 16, August 15 and August 17.
• Vikram also guessed the date at this point which means that out of the options left even the month shouldn't be repeated otherwise Vikram would have been confused and not been able to guess.
• So, it is not August 15 or August 17.
• Hence July 16 is the correct answer.