How many times will  be used the digit 7 if someone writes down all the numbers from 1 to 1000?

Find all pairs of positive integers to replace the numerators "* " to satisfy equation:
*/7 - */9 = 1/63

Find a real number, which exceed its square by the maximum value.

There are 3 boxes with balls inside them. They are labeled “two whites”, “two blacks” and “black and white” to show the contents of the boxes. Someone changes the labels to make them all false. Find the contents of each box by removing only one of the balls.

What the hell is this?     

You have N x N chess board?       How many squares would be in total on this board?

Stare at the dot in the center and move your head in and out. How it could be possible?