How many words can a pen with half refill write?

John gave half of the apples he had plus one more to Jacob. He gave half of the remaining ones plus one more to James. Now, John was left with just one apple.

Can you find out how many did he have in the beginning?

Here is a mathematical expression that also secretly tells a movie name. What movie is that?

You are given four results as below:
1111 = F
2222 = E
3333 = T
Then, can you find out how to code 4444?

A person is found murdered in his Chamber. When the crime scene is investigated, the Investigator find out that there is a calendar on which the victim has written a few numbers with his blood. The numbers are 4, 11, 11 and 4.

There are four suspects in the murder, John, Jacob, Anna and Lee. Can you find out who is the murderer?

I make two people out of one. What am I?

You see me once in June, twice in November, and not at all in May. What am I?

What is a word made up of 4 letters, yet is also made up of 3. Sometimes is written with 9 letters, and then with 4. Rarely consists of 6, and never is written with 5.

What is the word or phrase?

Write the next letter in this sequence.
O, T, T, F, F, S, S, E, __
**Hint: It is a Number Series Puzzle