How can you make number one disappear by adding something to it?

Find the missing number in the sequence below:

Mr Black, Mr Gray, and Mr White are fighting in a truel. They each get a gun and take turns shooting at each other until only one person is left. Mr Black, who hits his shot 1/3 of the time, gets to shoot first. Mr Gray, who hits his shot 2/3 of the time, gets to shoot next, assuming he is still alive. Mr White, who hits his shot all the time, shoots next, assuming he is also alive. The cycle repeats. If you are Mr Black, where should you shoot first for the highest chance of survival?

There is a square of a particular number which when doubled, becomes 7 more than its quarter.

Can you find the number?

Can you solve the tricky chess rebus puzzle below by ciphering the hidden meaning?

Keyboard words are not in alphabetical order, Why?

I look at you, you look at me, I raise my right, you raise your left. What am I?

I am the fastest animal but cannot climb the tree. What am I?

Can you name some countries which do not have the alphabet 'A' in them?

What can you deduce from the following BrainBat?

CRY
LMKI