Fun Mathematical Problems I

15 Points Per Correct Answer - No time limit  

1. I don't know you and you don't know me. But I know how big is the probability that we both celebrate our birthday on the same day. And you? Answer: (number : number with a colon between numbers- assume regular years, not leap years)

2. A teacher has 10 pupils in his classroom. He has 1 gift to give to one of his students. He writes down a number on a piece of paper and says to the first student: pick a number between 1 and 10, if you guess the number then you get the present... If not, I'll continue with the rest of the class. The boy in the back starts crying and says 'it is not fair, I don't have an equal chance'. Supposing no one picks the same number twice, is he (the boy) right? Answer: (yes or no)

3. Fill in the blank: 1, 2, 3, 5, 8, 13, 21, ... ? Answer: (number)

4. Can 234567 be divided by 9 (resulting in a natural number, that is)? Answer: (yes or no)

5. Fill in the blank: 0, 2, 6, 14, 30, ... ? Answer: (number)