MathNet 2019-part-02 — 184 problems (EN–VI) Question 11

A number is called TOP if it has 5 digits and the product of the first and the fifth digits equals the sum of the second, third and fourth digits. For example, $12338$ is TOP, since it has 5 digits and $1 \cdot 8 = 2 + 3 + 3$.

a) What is the value of $a$ for $\overline{234a8}$ to be TOP?

b) How many TOP numbers end in 2 and begin with 1?

c) How many TOP numbers begin with 9?