Ben and Mark are students of Mr Tan. Mr Tan’s date of birth is on N/M/1970 and both of them know that Mr Tan’s birthday is one of these 10 dates:
4/3/1970 5/3/1970 8/3/1970 4/6/1970 7/6/1970 1/9/1970 5/9/1970 1/12/1970 2/12/1970 8/12/1970
Mr Tan tells Ben the value of M and tells Mark the value of N. Then Mr Tan asks them: “Do you know when my birthday is?”
Ben says: “I don’t know, but I can be sure that Mark doesn’t know either.”
Mark says: “Initially I don’t know, but now I do.”
Ben says: “Oh, then now I know it too.”
Based on this dialogue and the dates given, can you figure out which is the correct date of Mr Tan’s birthday?
Mr Tan’s birthday is on 1/9/1970.
N and M represent the day and month of a date respectively.
Ben can only know the date if he is given a unique M. There are no unique M’s. Mark can only know the date if he is given a unique N. There are two unique N’s: 7 and 2. Since Ben can ensure that Mark doesn’t know, we know Mark can’t have any M that corresponds to the unique N’s. So, this eliminates June and December.
We are now left with March and September:
4/3/1970 5/3/1970 8/3/1970 1/9/1970 5/9/1970
So Mark either has 1, 4, 5, or 8. Since Mark is able to determine the date, the day has to be unique. If Mark was told 1, he knows it’s 1/9/1970. If he was told 4, it’s 4/3/1970. If he got 8, it’s 8/3/1970. If he had been told 5, there is not enough information as it is not a unique, so it cannot be 5.
So, we are now left with:
4/3/1970 8/3/1970 1/9/1970
And finally, since Ben can identify the birth date at this point, this means that there must be only one unique month value left which would eliminate 4/3/1970 and 8/3/1970, leaving 1/9/1970 as the correct birth date.