A man would like to take a new health insurance. An officer taking care of these matters says to the man: "Please tell me how many children you have." The man answers: "I have three of them." The officer: "What are the ages of your children?". The man answers: "The product of the ages is equal to 36." The officer replies: "This is not enough information Sir!". "Sorry that I was a little bit unclear, but the sum of the ages is equal to the number of shops in front of your office," says the man. The officer: "This still isn't enough information Sir!". The man replies: "My oldest child loves chocolate." The officer: "Thanks for your cooperation, I now know the ages."
Are you as smart as the officer? Then give the ages of the children.

Suppose you have five bags filled with the same type of coins and a weigthing machine. One of this bags is completely filled with fake coins, the other bags contain only real ones. A real coin weights 10 gram and a fake one 11 gram. What is the minimal number of times you need to use the weighting machine in order to find the bag with the fake coins?

What are the next numbers in the following sequences?
a: 77, 143, 221, 323, 437
b: 1, 5, 32, 288, 3413
c: 827, 23, 11, 6, 3
d: 2, 3, 5, 11, 31
e: 100, 121, 144, 202, 244