Jill is a very friendly girl who always has high expectations from her friends. Particularly when it comes to celebrating birthdays, Jill remembers the birthdays of all her friends on her fingertips, and she loves to plan the birthday parties for all her friends.
Two of Jill’s closest university friends Becky and James have been so busy doing their research thesis that they lost track of Jill’s upcoming birthday. Actually Jill told them her birthday in their very first interaction that was few months ago. However not everyone could have a memory like Jill’s. So when Jill invited them to her birthday, Becky asked “when are you celebrating”. That question made Jill furious and she said “If you do not even remember my birthday, you aren’t invited”. Jill walked away and then stopped. She turned around and said “I am giving you 10 dates and one of them is my birthday. Also I will tell Becky the month of my birthday and James will only be told the date of my birthday. If you can recall from this clue in next 5 minutes, you are welcome to the party, else you both can get lost”.
Jill then gives them a list of 10 possible dates as follows:
- May 15 – May 16 – May 19
- June 17 – June 18
- July 14 – July 16
- August 14 – August 15 – August 17
After having a look at the dates, Becky and James still couldn’t recall Jill’s birthday.
Jill then separately tells Becky and James the month and the day of her birthday respectively. Jill said “You can’t reveal your piece of information to each other. And your 5 minutes start now”.
Becky: I don’t know when Jill’s birthday is, but I know that James does not know too.
James: At first I didn’t know when Jill’s birthday is, but I know now.
Becky: Oh now I also know when is Jill’s birthday.
To Jill’s surprise Becky and James told her birthday within few minutes.
Can you also tell when is Jill’s birthday as discovered by James and Becky ?
——- View the answer ——–
First statement meant that there must be 2 possible months for every date in the birthday month. As if there was just one possible month to the birthday date, James would know the answer because he would have known both the date and the month. So, we can eliminate any month with a date that is not repeated in another month. We can eliminate May because 19 is not repeated and June because 18 is not repeated.
Now, second statement gives us a smaller set of possible dates, as James can now tell when is the Jill’s birthday. This means that we can eliminate all days that are in both months, which are July and August 14th.
Third statement tells us that now Becky also knows Jill’s birthday, so there must be only one date left in a month for her to know that.
This means that the date of Jill’s birthday is July 16th.
