Roberto wants to write the number 111111 as a product of two numbers, neither of which ends in 1. Is this possible? Why?
Factoring 111111, we obtain $111111=3 \times 7 \times 11 \times 13 \times 37$. It follows that it is indeed possible to write the number 111111 as a product of two factors, neither of which ends in 1. For example, $111111=3 \times 37037$. But there are other possibilities, such as, for example, $111111=7 \times 15873$.

In fact, it is possible to list all the possibilities. They are

$$
\begin{array}{lllll}
3 \times 37037, & 7 \times 15873, & 13 \times 8547, & 33 \times 3367, & 37 \times 3003 \\
39 \times 2849, & 77 \times 1443, & 143 \times 777, & 259 \times 429 \quad \text { and } & 273 \times 407
\end{array}
$$

Therefore, Roberto has 10 options to write 111111 in the desired form.