### 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.

### QUESTION 6:

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 ) =