Math Riddles

Albert and Bernard became friends with Cheryl, and they want to know when her birthday is. Cheryl gives them a list of 10 possible dates.

May 15      May 16      May 19
June 17     June 18
July 14     July 16
Aug 14      Aug 15      Aug 17

Cheryl then tells Albert and Bernard separately the month and the day of her birthday respectively.

Albert: I don’t know when Cheryl’s birthday is, but I know that Bernard does not know too.
Bernard: At first I don’t know when Cheryl’s birthday is, but I know now.
Albert: Then I also know when Cheryl’s birthday is.

When is Cheryl’s birthday?

Two schoolgirls were traveling from the city to a dacha (summer cottage) on an electric train.

“I notice,” one of the girls said, “that the dacha trains coming in the opposite direction pass us every 5 minutes. What do you think-how many dacha trains arrive in the city in an hour, given equal speeds in both directions?”

“Twelve, of course,” the other girl answered, “because 60 divided by 5 equals 12.”

The first girl did not agree. What do you think?