Birthday dates

Logic Level 2

Alfred and Ben just became friends with Clarke, and they want to know when her birthday is. Clarke gives them a list of 10 possible dates.

Clarke then tells Alfred and Ben separately the month and the day of her birthday respectively.

Alfred: I don't know when Clarke's birthday is, but I know that Ben does not know too.
Ben: At first I didn't know when Clarke's birthday is, but I know now.
Alfred: Then I also know when Clarke's birthday is.

So when is Clarke's birthday?

May 15 June 17 July 16 August 14

1 solution

Chew-Seong Cheong
Oct 21, 2019

Alfred: I don't know when Clarke's birthday is, but I know that Ben doesn't know too.

Alfred would not know when Clarke's birthday is whichever month he was told. He was sure that Ben would not know too because the month he got was not May or June. If it was May or June, it was possible for Ben to know the birthday if the date he got was 18 or 19 (for June or May respectively). Therefore, the birth month was either July or August.

Ben: At first I didn't know when Clarke's birthday is, but I know now.

Knowing that the month was either July or August, Ben then knew the birthday. This means that he did not get 14 as the date. If he got 16 then the birthday would be July 16. If he got either 15 or 17, the birth month would be August.

Alfred: Then I also know when Clarke's birthday is.

Alfred knew that Ben did not get 14 as the date, else Ben would not know the birthday. But if Alfred got August as the month, then he still would not know the birthday, because Ben could have either 15 or 17 as the date. Alfred knew the birthday because he got July as the month and the birthday could only be July 16 .