If 21x = 79x, what is the value of x?

You can find some missing letters in the picture. By placing two particular letters in the spaces, you can form a nine lettered word beginning from one of the corners and going clockwise direction to the middle. Can you find out the letters and the word?

What is more useful when it is broken?

We have arranged an array of numbers below. What you have to do is use any kind of mathematical symbol you know excluding any symbol that contains a number like cube root. You can use any amount of symbols but you have to come up with a valid equation for all of them.

0 0 0 = 6
1 1 1 = 6
2 + 2 + 2 = 6
3 3 3 = 6
4 4 4 = 6
5 5 5 = 6
6 6 6 = 6
7 7 7 = 6
8 8 8 = 6
9 9 9 = 6

I possess a head

I flaunt a tail

But I don't have mouth or legs

Can you find out who I am?

If we tell you that there is a relation between the numbers and letters in the given figure, can you analyze it and find the missing letter in the last box?

If you had an infinite supply of water and 5-quart and 3-quart pails, how would you measure exactly 4 quarts? What is the least number of steps you need?

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?

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

Using eight eights and addition only, can you make 1000?