(lifted from someone else's blog)
Boys A and B are students of Miss X, whose birthday is on the Nth day of the month, M.
Both students know that her birthday falls on one of the following dates:
March 4th, March 5th, March 6th
June 4th, June 7th
September 1st, September 5th
December 1st, December 2nd, December 6th
Miss X only told A the month and B the day. She then asked them both if they knew her birthday.
Here's what the boys said:
A: If I don't know the answer, B would confirm not know.
B: At first I didn't know, but I do know now.
A: Oh, then I know the answer too.
What's the birthday of Miss X?
Answer to the quiz:
First and foremost, you have to look at this question from 3 perspectives: A, B and yourself as the reader.
Also, you have to assume that all 3 are intelligent. At least, that was what I assumed myself to be, which was a pretty simple thing to do.
So, how do you tackle this question? Simple. By process of elimination.
Miss X told A the month and B the day. Now, if you look at the days provided from the choices, you'll notice there are two unique days: 2nd and 7th.
Let's see how I solved it:
1. Look at the very first statement that A said: "If I don't know the answer, B would confirm not know."
From this very statement, I eliminated all the dates from the months of June and December. Why? Assume Miss X told A her birthday's month was December. If that is the case, how can A then proclaim that B would confirm not know the answer? At this point in time, it is true that A doesn't know the answer because it might be Dec 1st, Dec 2nd or Dec 6th. But how does he know if B does not hold the day to be 2nd? Remember 2nd is a unique day. Similarly for June, assuming Miss X told A her birthday's month was June, she could easily have told B the day to be 7th, which is the unique day as well.
Therefore, if indeed the month is either June or December, A will not be able to make that statement that B would confirm not know.
2. Now we're left with the months of March and September.
Take a look at what B said next: "At first I didn't know, but I do know now."
Remember the assumption that these boys are intelligent? B would have followed the thought process of A and know that the months cannot be June or December.
However, upon following A's train of thought, he manages to derive at the answer. From this, I eliminated the dates March 5th and September 5th. Why? If at this point in time, B does hold the number 5, he will also not be able to proclaim that he knows the answer now. Because obviously, if he holds the number 5, A can hold either March or September and Miss X's birthday is still pretty much in the air. The fact that B now knows the answer means March 5th/September 5th cannot be the answer.
3. Now we're left with the following 3 dates: March 4th, March 6th and September 1st.
What does A say next? "Oh, then I know the answer too."
Once again, as the intelligent reader, you will know that A has also followed B's thought process and came up with the remaining 3 dates to choose from. Now, if A was holding the month March, he would not be able to proclaim that he knows the answer too. Because obviously, it can either be March 4th or March 6th.
Therefore, the answer has got to be September 1st.
posted by bert @ 12:05 AM
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