I am a seven-letter word but if you remove four of my letters I will have one left. What word am I?

Can you figure out the logic I used to decide the order of the following words:
gun, shoe, spree, door, hive, kicks, heaven, gate, line, den

A high school has a strange principal. On the first day, he has his students perform an odd opening day ceremony:

There are one thousand lockers and one thousand students in the school. The principal asks the first student to go to every locker and open it. Then he has the second student go to every second locker and close it. The third goes to every third locker and, if it is closed, he opens it, and if it is open, he closes it. The fourth student does this to every fourth locker, and so on. After the process is completed with the thousandth student, how many lockers are open?

A network of 20 x 10 squares is given to you.

Can you calculate how many unique squares and rectangles can be formed combining two or more individual squares ?

A crime was committed at baker street. Ibrahim Dakota who was shot in the stomach was the main suspect. Sherlock questioned the suspect. The conversation started as:
Sherlock: What's your story, Ibrahim?
Ibrahim: I was walking around baker street and suddenly a man from the back shot me. I ran as fast as I could to save my life".
Sherlock: That is enough (and ask the police to arrest him).

Why does Sherlock think he is the murderer?

What can run but never walk, have a mouth that never speaks, have a head that never weeps, and have a bed but never sleeps?

Find the next number in the sequence

1, 2, 6, 21, 88, __?

You order chicken wings at KFC in the boxes of 6, 9 and 20. What is the largest number of wings that you cannot obtain by buying in any combination of the boxes?

If 5 cats catch 5 mice in 5 minutes, how long will it take one cat to catch a mouse?

Identify the 10 differences between the two given pictures.