Only one color, but not one size,
Stuck at the bottom, yet easily flies.
Present in sun, but not in rain,
Doing no harm, and feeling no pain.
What is it?

I am Huge on Sunday and Saturday.
I am small from Tuesday to Thursday.
I do not exist on Monday and Friday.
Who am I?

What does this simple rebus mean?

A swan sits at the center of a perfectly circular lake. At an edge of the lake stands a ravenous monster waiting to devour the swan. The monster can not enter the water, but it will run around the circumference of the lake to try to catch the swan as soon as it reaches the shore. The monster moves at 4 times the speed of the swan, and it will always move in the direction along the shore that brings it closer to the swan the quickest. Both the swan and the the monster can change directions in an instant.
The swan knows that if it can reach the lake's shore without the monster right on top of it, it can instantly escape into the surrounding forest.

How can the swan successfully escape?

I’m tall when I’m young, and I’m short when I’m old. What am I?

Four men were in a boat on the lake. The boat turns over, and all four men sink to the bottom of the lake, yet not a single man got wet! Why?

Sherlock breaks into a crime scene. The victim is the owner who is slumped dead on a chair and have a bullet hole in his head. A gun lies on the floor and a cassette recorder is found on the table. On pressing the play button, Sherlock hears the message 'I have committed sins in my life and now I offer my soul to the great Lord' and followed a gunshot Sherlock smiles and informed the police that's its a murder.

Why did he think so?

There are nine letters in the below-given diagram. You have to form a nine-letter word using these letters.

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

Can anyone explain, how is this possible?

Can you solve below mathematical equation?

2^1234 - 2^1233