How many words can a pen with half refill write?

What are the 50th, 63rd and 100th numbers in the sequence below?
4, 5, 8, 8, 9, 9, 12, 13, 13, 13, 17, 18, ...

Complete the series by replacing "?" with the correct number.

ST ND RD TH '?'

Nodes are shown below and you need to connect them based on the following rule: Every node can be connected to the number of nodes inside them, i.e. the first node there is a value of 1 which indicates that the first node can connect to exactly one node only.Can you do it?

10 people came into a hotel with 9 rooms and each guest wanted his own room. The bellboy solved this problem.
He asked the tenth guest to wait for a little with the first guest in room number 1. So in the first room, there were two people. The bellboy took the third guest to room number 2, the fourth to number 3, ..., and the ninth guest to room number 8. Then he returned to room number 1 and took the tenth guest to room number 9, still vacant.
How can everybody have his own room?

Irene killed hundreds of people mercilessly and yet the police were not able to put her behind the bars. Why?

It is always ahead of me yet I can never see it. What is it?

A man was found murdered on Sunday morning. His wife immediately called the police. The police questioned the wife and staff and got these alibis: The Wife said she was sleeping. The Cook was cooking breakfast. The Gardener was picking vegetables. The Maid was getting the mail. The Butler was cleaning the closet. The police instantly arrested the murderer. Who did it and how did they know?

Rebus Puzzle Definition: A rebus is an illusion device that uses pictures to represent words or parts of words.
What does This Rebus Puzzle Identify?

Highly detail-oriented individuals excel at this type of optical illusion challenge. It requires not just good eyesight but also the ability to distinguish subtle differences quickly. Finding the 6 among all these 9's could indicate a high level of IQ and superior observational skills.