Recently, while in London, I decided to walk down the escalator of a tube station. I did some quick cal-culations in my mind. I found that if I walk down twenty-six steps, I require thirty seconds 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?

We have a circular dining table made of marble which has come down to us as a family heirloom. Ws also have some beautiful bone-china saucers that I recently brought from Japan.
Our table top is 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 over lap each other nor the edge of the table.
How many can we place in this manner?^