149. Scattered set. In a printing house, a multiplication line of the form $\overline{a b c} \cdot \overline{b c a} \cdot \overline{c a b}^{*}$ was being set; but the set scattered, and the digits of the product got mixed up. As a result, the product was printed as 2342355286. It is known that $a>b>c$ and that the units digit of the printed product is the correct digit 6. Restore the true value of the product.
149. Let $n=a b c$, and $N$ be the desired product. If $c=1$, then the largest possible $n$, namely 981, would yield a product $N=159080922$, which is too small. Therefore, $982 \leqslant n \leqslant$ 987. The sum of the digits of $N$ is $35 \equiv 2(\bmod 3)$; hence, $n$ and the numbers obtained by permuting the digits of $n$ give a remainder of 2 when divided by 3. Thus, $n$ is either 986 or 983. However, a 6 in the units place of the product will only occur if $n=983$. Therefore, the correctly typed line should be

$$
(983)(839)(398)=328245326
$$

[W. R. Talbot, A. M. M., 66, 726 (October 1959).]