Question 190
Let $n \le 100$ be a positive integer. There are 101 numbers written in a row:
$$
0 \cdot n \text{ mod } 101, 1 \cdot n \text{ mod } 101, \dots, 100 \cdot n \text{ mod } 101.
$$
How many pairs of neighbouring numbers are there in this row such that the one on the left is bigger than the one on the right?
$$
0 \cdot n \text{ mod } 101, 1 \cdot n \text{ mod } 101, \dots, 100 \cdot n \text{ mod } 101.
$$
How many pairs of neighbouring numbers are there in this row such that the one on the left is bigger than the one on the right?