October 2013 Maths Challenge

A ball is dropped 128 feet from the roof of a building. Suppose that with each bounce, the ball goes up exactly half its previous height. A woman is sitting at her desk on the second floor. How many times will she see the ball if her eye level is 15 feet above the ground?
Suggested solution:
Seven times. The ball drops 128 ft. and then bounces to a height of 64 ft. The subsequent bounces are 32 ft. and 16 ft, after which the woman no longer sees the ball. The ball is seen twice for each bounce, going up and falling down, and once for the initial drop. Drawing a picture of the situation can help you track the number of times the woman sees the ball.

** The winner of the October Maths Challenge was Ava Rooney of Donabate Community College. Ava was named Mathematician of the Month and won a gift voucher worth EUR100. **