I am quite hot but become too cold if you remove the first two letters. What am I?

There are five people. One of them shot and killed one of the other five.
We know following clues:
1. Dan ran in the NY City Marathon yesterday with one of the innocent men.
2. Mike consider being a farmer before he moved to the city.
3. Jeff is a top notch computer consultant and wants to install Ben new computer next week.
4. The murderer had his leg amputated last month.
5. Ben met Jack for the first time six months ago.
6. Jack has been in seclusion since the crime.
7. Dan used to drink heavily.
8. Ben and Jeff built their last computers together.
9. The murderer is Jack's brother. They grew up together in Seattle.

Consider yourself to be a famous detective "Sherlock Homles", Can you find the killer?

What word is represented by this rebus?

Count the number of triangles in the given picture.

What word is identified by the below rebus?

Your Your Your Your Your
Your Your Your Your Your

Below, you can see three complete equations and one incomplete. Based on the three complete ones, can you complete the incomplete one?

5 $ 4 $ 3 $ 9 = 4215
6 $ 9 $ 2 $ 6 = 3816
4 $ 7 $ 3 $ 3 = 1122
7 $ 2 $ 7 $ 4 = ____

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

John can place six large boxes or nine small boxes into a carton.

Can you find out in how many cartons can he place sixty-six boxes in total?

I am the one who remains awake when you sleep. But I need to rest when you awake. Who Am I?

There is an English word that can be used up to four times in a row without modifying the spelling and form a valid grammatical sentence.

Do you know what word is that?