Problem

Source: 1998 Estonia National Olympiad Final Round grade 9 p3

Tags: algebra, number theory, combinatorics



On a closed track, clockwise, there are five boxes $A, B, C, D$ and $E$, and the length of the track section between boxes $A$ and $B$ is $1$ km, between $B$ and $C$ - $5$ km, between $C$ and $D$ - $2$ km, between $D$ and $E$ - $10$ km, and between $E$ and $A$ - $3$ km. On the track, they drive in a clockwise direction, the race always begins and ends in the box. What box did you start from if the length of the race was exactly $1998$ km?