Chapter 4, Problem 4NT

NOW TRY THIS 4

Colored rods are used in the elementary school classroom to teach many concepts. The rods vary in length from $1\text{cm}$ to $10\text{cm}$. Various lengths have different colors; for example, the $5$ rod is yellow. The rods and their colors are shown in Figure $8\left(a\right)$. A now with all the same color rods is called one-color train.

a. What rods can be used to form a one-color train for $18$?

b. What one-color trains are possible for $24$?

c. How many one-color trains of two or more rods are possible for each prime number greater than $7$?

d. In figure $8\left(b\right)$, a number represented by an all-red train, an all-green train, and all-purple train is shown. How many factors does this number have? What are the factors?