If you have a piece of straightedge 121 centimeters long, how
can you cut it into five pieces so that you can measure any integral centimeter
distance of 1 to 121 centimeters. You can only use once each smaller
straightedge you cut during the measurement.
Solution: Cut the straightedge into five pieces with
lengths of 1 cm, 3 cm, 9 cm, 27 cm, and 81 cm. These lengths are powers of