## 9. Cigarettes

Four married couples had dinner together. After dessert, Diana smoked three cigarettes, Elizabeth smoked two, Nicole smoked four, and Maud smoked one cigarette. Simon smoked as many as his wife, Pierre smoked twice as many as his wife, Louis smoked three times as many as his wife, and Christian smoked four times as many as his wife.

If all the people present smoked a total of 32 cigarettes, could you tell me the name of Louis's wife?
9. If all the people present together smoked 32 cigarettes, then the share of the four men is 22 cigarettes. We need to represent the number 22 in the following form:

$$
22=1 \cdot x+2 \cdot y+3 \cdot z+4 \cdot t
$$

where $\{x, y, z, t\}=\{1,2,3,4\}$ (these are the numbers of cigarettes smoked by the four ladies). But there is only one such representation of the number 22:

$$
22=(1 \cdot 3)+(2 \cdot 4)+(3 \cdot 1)+(4 \cdot 2)
$$

Therefore, Louis, who smoked three times as many cigarettes as his wife, is married to Maud, who smoked only one cigarette.