The minimum number of assignments to "indexsmallest" once the outer loop starts, in a selection sort algorithm for sorting a list with 21 elements, is 20.
In selection sort, the outer loop iterates n-1 times, where n is the number of elements in the list. In this case, n = 21, so the outer loop iterates 20 times.
In each iteration of the outer loop, the inner loop is used to find the smallest element in the unsorted portion of the list. The variable "indexsmallest" is used to store the index of the smallest element. The minimum number of assignments to "indexsmallest" is one per iteration of the outer loop, so the total minimum number of assignments is equal to the number of iterations of the outer loop, which is 20 in this case.