Editor
1. Fix a positive integer \(\displaystyle n\) and write the numbers \(\displaystyle 0, 1, \ldots, n-1\) on a whiteboard in some order. Two numbers form an inversion if the greater precedes the smaller. A number \(\displaystyle k\) is called special if \(\displaystyle k\) forms inversions with exactly \(\displaystyle k\) other numbers. At most how many special numbers can we have on the board?
