Albert and Bernard just becone 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   

     August 14    August 15   August 17

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

  Albert: I don't know when Cheryl's birthday is, but I know that Bernard does not knnow 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.

So when is Cheryl's birthday?

At first, the problem seems impossible to solve. But once you use some logic, the solution is actually rather simple. Rattle your brain — or phone a friend — before I send the solution in 1+ hour 

(P/s: The question was originally thought to posed to fifth graders competing in the Singapore and Asean Schools Math Olympiads (SASMO).)

Two barrels X and Y contained different amounts of oil at first. Some oil from X was poured to Y so that the amonut of oil in Y was doubled. Then, some oil from Y was poured to X so that the amount of oil in X was doubled. After these two pourings, the barrels each contained 18 litres of oil. How many litres of oil were in X at first?

Placed on a table is a mathematics problem:

       89 + 16 + 69 + 6\(\Delta\) + \(\bigcirc\)8 + 88,

where each of the symbols \(\Delta\) and \(\bigcirc\) represents a digit. Two students A and B sit on the opposite sides ò the table facing each other. They read the problem from their direction and both get the same answer. What is the answer?