3. The length of the road from the Capital to city O is 2020 kilometers. Along the road are kilometer markers. On the first marker, on the front side, 1 is written, and on the back - 2019; on the second - 2 and 2018 ..., on the last - 2019 and 1. A marker is called good if the two written numbers have a common divisor other than 1, otherwise it is called bad. How many bad markers are there along this road?
3. Answer: 800. Solution. Note that the sum of two numbers on a pillar is 2020. If both numbers are divisible by some common divisor, then $2020=4 * 5 * 101$ is also divisible by this divisor. All even pillars are good, all divisible by 5 are good, all divisible by 101 are good. In total, there are odd pillars $2020 / 2=1010$. Among them, not divisible by 5 are $1010 * 4 / 5=808$. Among them, not divisible by 101 are $808 * 100 / 101=800$ (this is the number of all bad pillars).

Grading criteria. Full solution - 7 points. It is noted that the divisors of good pillars are the divisors of the number 2020 - $\mathbf{1}$ point. Part of the divisors is correctly excluded, but not all - up to 3 points. Answer without explanation - $\mathbf{0}$ points.