Jill is a friendly girl with high hopes for her friends. She’s big on birthday celebrations remembering everyone’s special day without fail. She enjoys putting together parties for all her pals.
Two of Jill’s closest college buddies, Becky and James, got so caught up in their research papers that they forgot about Jill’s upcoming birthday. Jill had told them her birthday when they first met a few months back. But not everyone has a memory like Jill’s. So when Jill invited them to her birthday, Becky asked, “When are you celebrating?” This question made Jill angry and she said, “If you can’t even remember my birthday, you’re not invited.” Jill stormed off but then stopped. She turned around and said, “I’ll give you 10 dates and one of them is my birthday. Also, I’ll tell Becky the month of my birthday and James will know the date of my birthday. “If you can remember from this hint in the next 5 minutes, you’re invited to the party otherwise 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.
