A good answer might be:

The base case is when a rock fragment is small enough. No more work needs to be done.

Recursion with Triangle Numbers

Here are the two parts to recursion:

  1. If the problem is easy, solve it immediately.
    • An easy problem is a base case.
  2. If the problem can't be solved immediately, divide it into smaller problems, then:
    • Solve the smaller problems by applying this procedure to each of them.

And here is how this applies to triangle numbers:

  1. Triangle( 1 ) = 1
  2. Triangle( N ) = N + Triangle( N-1 )

The problem "Triangle(N)" is divided into two problems: "add N to something" and "Triangle(N-1)". Sometimes the latter can be solved immediately (when it is the base case). Other times you need to re-apply the solution to the smaller problem.


Using the above, what is Triangle(3)? (Fill in the boxes starting with the top row and work your way down.)

Triangle( 3 ) = + Triangle( )
Triangle( 2 ) = + Triangle( )
Triangle( 1 ) =      
Triangle( 2 ) = +
Triangle( 3 ) = +
Triangle( 3 ) =