From the sequence $1,2, \ldots, 100$, we want to produce the sequence $2,3,4, . ., 99,100,1$ by performing steps in which we swap two | not necessarily adjacent | elements. What is the minimum number of steps required?
In a swap, the positions of two elements change; one moves forward, the other moves backward. Among the elements of the sequence, 99 elements $(2,3, \ldots, 100)$ need to move forward at least once, so fewer than 99 swaps are definitely not enough.

However, the desired order can be achieved in 99 steps, for example, if we always swap the 1 with the number immediately following it.