11 plus the number of pins in 10 rows.
This keeps on going. For any N
greater than one,
you can divide the problem into an integer
and a problem that is smaller by one.
Eventually you reach the end:
number of pins in 12 rows = 12 + number of pins in 11 rows number of pins in 11 rows = 11 + number of pins in 10 rows number of pins in 10 rows = 10 + number of pins in 9 rows . . . number of pins in 3 rows = 3 + number of pins in 2 rows number of pins in 2 rows = 2 + number of pins in 1 row number of pins in 1 row = 1
The number of pins in 1 row is called a base case. A base case is a problem that can solved immediately. In this example, the base case is: the number of pins in 1 row is 1.
Once you have reached the base case, you can work your way back up to the original problem.
What is the result of this addition (use the base case):