## 43. Rue Saint-Nicaise

On December 24, 1800, First Consul Bonaparte was heading to the Opera along Rue Saint-Nicaise. A bomb exploded on his route with a delay of a few seconds. Many were killed and wounded. Bonaparte accused the Republicans of the plot; 98 of them were exiled to the Seychelles and Guiana. Several people were executed. Suppose the number of wounded is equal to twice the number of killed (in the explosion) plus four-thirds of the number of those executed, that the sum of the number of killed or wounded and the number of those executed is slightly less than the number of those exiled, and that if you subtract 4 from the number of killed, you get exactly twice the number of those executed.

Could you, without referring to history books, determine how many people Bonaparte executed after the attack on Rue Saint-Nicaise?
43. Let $x$ be the number of those executed; then, according to the last condition of the problem, the number of those killed in the explosion is $2 x+4$, and the number of wounded is

$$
2(2 x+4)+(4 / 3) x=5 x+x / 3+8
$$

(hence, $x$ is a multiple of 3).

It is also known that

$$
(2 x+4)+(5 x+x / 3+8)+x<98
$$

or

$$
x<10
$$

Since $x$, on the one hand, is slightly less than 10, and on the other - a multiple of 3, then, apparently, $x=9$.

Thus, after the assassination attempt on the rue Saint-Nicaise, Bonaparte executed nine republicans.