A former high school student, Lorena, brought this question to me for her college algebra class for elementary school teachers. We worked it out by hand for the first few days (as that met the need of her assignment). However, I wanted to be able to take it a step further, and speed the process up, by clicking through each day.

Below was the prompt:

Two brothers inherit a large field. They decide to split the field perfectly in half. However, later that night the younger brother feels that his older brother deserves more, and so without telling him, he gives his older brother one third of his portion. The older brother, has the same thought, and decides to give his brother one third of his land (not realizing that his current land was more than half of the field because of the gift from his brother).

What percent of the entire field does the younger and older brother now own?

What if the brothers continued giving one third of their field to the other each night, what percent would each own after ten nights?

Additional thoughts for the web app:

Allow the user to enter an arbitrary day with out having to click through.