Alex and Bob befriended a girl. They ask her what is her birthday. She does not give a straight forward answer, but gives some hints.
She gives them the following 10 dates to pick her birthday
· May:15,16,19
· June:17,18
· July:14,16
· August:14,15,17
Then she discloses her correct month to Alex and correct date to Bob.
Asks Alex to guess the right birthday. He says sorry I can’t but I’m sure even Bob won’t be able to guess it right.
Now Bob says, I was a bit confused but with Alex’s statement, I know what is her birthday.
Now Alex says if that is the case, I also know what is it.
Both guessed it right.
What's the birthday
Answers
Given : list of 10 Dates . and month told to Alex and date told to Bob
To find : Exact Date of Birth
Solution:
Dates
MAY 15 , 16 , 19
JUNE 17 , 18
JULY 14 16
AUGUST 14 , 15 , 17
Alex knows month only so Alex does not know the correct date of birth
as each month has more than one date
But Alex say Bob also do not know the correct date of birth
hence the Month known to Alex does not have unique date ( which is only in a particular month like 18th june & 19th May)
hence MAY & JUNE can not be Month
So now Bob knows that
Month is JULY or AUGUST only ( which was not known to him earlier)
14 Can not be date as then Bob would not know which month ( July or august)
Hence possible date are 16 JULY , 15 AUGUST & 17 AUGUST
but now Alex says he also know date of birth
it means month is not august as if it would have been august then Alex could not know which date
Hence 16 JULY is the DOB
Her birthday on 16 July
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