Suppose you want to make a path between each number on Pascal's Triangle. For this exercise, suppose the only moves allowed are to go down one row either to the left or to the right.

We will code the path by using bit strings. In particular, a 0 will be used for each move downward to the left, and a 1 for each move downward to the right. So, for example, consider the first five rows of Pascal's Triangle below, and the path shown between the top number 1 (labeled START) and the left-most 3.

START Row Row 2 Row 3 3 001 O 4 6 4 Row 1 10 10 5 Row