Discussion: This student reformulates this problem so that instead of thinking about abstract numbers the quantities become a collection of rulers with lengths equal to the fibonacci numbers - one for each number.This is essentially an argument by induction.

Written response: Nice way to look at this. This is a plausible argument but needs to be made more rigorous. This can be done by using the principle that when you have some kind of process that might be arbitrarily long it can usually be replaced by an induction argument.

Click the image to bring up an enlarged copy of the solution.