Find the Next Number in the Sequence

2 9 3 1 8 4 3 6 5 7 ?

Whats the next number in the below number sequence pattern.

There are three boxes. One is labeled "APPLES" another is labeled "ORANGES". The last one is labeled "APPLES AND ORANGES". You know that each is labeled incorrectly. You may ask me to pick one fruit from one box which you choose.

How can you label the boxes correctly?

John was visiting his friend Jacob. He found out that his friend's wife had just killed a burglar in self-defense.
John asks Jacob about what happened and he told that "His wife was watching television when suddenly the bell rang. She thought that it is her husband Jacob but she found the burglar who attacked her instantly and she got so frightened that she killed the burglar immediately with the knife.
John asked the police to arrest his friend's wife. Why?

I had an infinite supply of water and 5 litres and 3 litres jars.

How would you measure exactly 4 litres in the least number of steps?

This is a famous paradox which has caused a great deal of argument and disbelief from many who cannot accept the correct answer. Four balls are placed in a hat. One is white, one is blue and the other two are red. The bag is shaken and someone draws two balls from the hat. He looks at the two balls and announces that at least one of them is red. What are the chances that the other ball he has drawn out is also red?

Replace the question mark in the picture below.

Solve the equation by replacing the alphabet with numbers.

MOM + MOM + NO = BOOK=

A man lives on the fifteenth floor of an apartment building. Every morning he takes the elevator down to the lobby and leaves the building. In the evening, he gets into the elevator, and, if there is someone else in the elevator, or if it was raining that day, he goes back to his floor directly. Otherwise, he goes to the tenth floor and walks up five flights of stairs to his apartment. Can you explain why he does this?

John is 45 years older than his son Jacob. If you find similarities between their ages, both of their ages contain prime numbers as the digits. Also, John's age is the reverse of Jacob's age.

Can you find their ages?