How can a man go eight days without sleep?

I am a ten letters word
The first four letters have the power to rule,
Next, four-letter can be eaten.
The next three-letter represents a lady.
I can fly as well

what am I looking for?

Can you write down eight eights so that they add up to one thousand?

The day after tomorrow will be three days before Tuesday. Can you find out what is today?

Can you arrange four 9's and use at most 2 math symbols, to make the total 100?

During a secret mission, an agent gave the following code to the higher authorities
AIM DUE OAT TIE MOD

However, the information is in one word only and the rest are fake. To assist the authorities in understanding better, he also sent them a clue, If I tell you any one character of the code, you can easily find out the number of vowels in the codeword.

Can you find out the code word?

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?

Do you know of a place where the wind blows south and then suddenly shifts direction towards the north?

Can you think of a smallest +ve number such that if we shuffle the digits of the number, the new number becomes double the original number?

The centre of the third figure is empty. What digit should fit inside?