Exercise 2. Anne drove her car for an integer (and non-zero) number of hours, and traveled an integer number of kilometers, at a speed of $55 \mathrm{~km} / \mathrm{h}$. At the beginning of the trip, the odometer read abc kilometers, where abc is a 3-digit number such that $a \geqslant 1$ and $a+b+c \leqslant 7$. At the end of the trip, the odometer read cba kilometers. Determine all possible values of the number abc.
Solution to exercise 2 Let d be the duration of the journey expressed in hours. We have $55 d=(100 c+10 b+a)-(100 a+10 b+c)=99(c-a)$. This simplifies to $5 d=9(c-a)$. This implies that $c-a$ is a multiple of 5. On the other hand, $c-a=5 d / 9>0$ and $c-a \leqslant c1$ then $c=5+a>6$ so $a+b+c>7$, which contradicts the assumption.

Therefore, the only possible value of abc is 106.