Maths - Which Date Is My Birthday

Charles and George are students of Mr. Smith. Mr. Smith's birthday is on D/M/1970 and both of them know that Mr. Smith's birthday is one of these 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. Smith tells Charles the value of M and tells George the value of D.

Then Mr. Smith asks them "Do you know when is my birthday?"

Charles says “l don't know, but I can be sure that George does not know too.'

George says "Initially, I don't know, but I know it now."

Charles says "Oh, then I know it too.”
Based on the dialogue and the dates given, can you figure out which date is Mr. Smith's birthday?


Check the answer below:

Charles first said he does not know because all the months appear more than once. When Charles said that he's sure that George does not know either, he's hinting to George that it is not the months of the dates that have no repetition.

Charles is assuming that if George knows within being first told, it means the date has no repetitions, which are 7/6 and 2/12. Charles is saying it is not the months 6 and 12.

So you first eliminate all dates with months 6 and 12

After elimination of months 6 and 12, you're left with 4/3, 5/3, 5/9, 8/3 and 1/9.

George was able to tell which date it is by now, meaning of these dates that are left; the day number does not have repetitions. 5/3 and 5/9 eliminated.

Left with 4/3, 8/3 and 1/9. Realise of these 3 options left, it cannot be 4/3 and 8/3 because the months are the same.