A dead body is found outside a multi-story multinational company. The case is reported and a homicide detective is called on the crime scene.

He looks at the body and then towards the building. From the position of the body, it is evident that the victim committed suicide. He goes to the first floor of the building and then walks in the direction of the dead body, opens the window and toss a coin in the air.

He goes to second floor and again repeats the process. He keeps doing this till he is done on all the floors. Then he returns back to the floor and tells his team that it is a murder.

How in heaven did he deduce that?

Begin with a word, five letters to my name,
Remove the first and last but I am the same
Take out my middle and still, I remain.
What word am I?

The following four words might seem abrupt to you. But you can make them meaningful by just adding vowels.
RDSH
GGPLNT
TMT
NN

Hint: All of them are vegetables.

The horse jumps over the king.
Strangely there is absolutely no scratch on him.

Can anyone explain, how is this possible?

I have an eye but still cannot see.

Who am I?

You are presented with three boxes. One of them has a red ball inside and the other two have a black ball inside each of them. You are asked to pick up the one with red ball and you pick one. Now, one of the other boxes is opened and it is found to have a black ball.

You are presented with a chance to change your box with the one that is left closed. Will you change your box? Why or why not?

Manish and Manoj play 5 games of chess.
Both Manish and Manoj win the exact same number of games. There is no tie at all.

How?

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

Two in a corner, one in a room, zero in a house, but one in a shelter. What am I?

Which three-digit number, made of consecutive digits, like 567, is 2 less than a cube and 2 more than a square?