What is my aunt’s share?

26.  The Round Table

We have a circular dining table made of marble which had come down to us as a family heirloom. We also have some beautiful bona-china saucers that I recently brought from japan.

Diameter of our table top id fifteen times the diameter of our saucers which are also circular. We would like to place the saucers on the table so that they neither overlap each other nor the edge of the table.

How many can we place in this manner?

27.  Down the Escalator

Recently, while in London, I decided to walk down the escalator of a tube station. I did some quick calculation in my mind. I found that if I walk down twenty-six steps, I required thirty second to reach the bottom. However, if I am able to step down thirty-four stairs I would only require eighteen seconds to get to the bottom.

If the time is measured from the moment the top step begins to descend to the time I step off the last step at the bottom, can you tell the height of the stairway in steps?

28.  The Chess Board

We all know that a chess board has 64 squares. This can be completely covered by 32 cardboard rectangles, each cardboard covering just 2 squares.

Supposing we remove 2 squares to the chess board at diagonally opposite corners, can we cover the modified board with 31 rectangles? If it can be done, how can we do it? And if it cannot be done, prove it impossible.

To view answer Click Here and check answers respectively to question number.