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We hold contests in mathematics, physics, and computer science.
Our contests have are of difficulty levels, and contestants may compete individually or in teams; details are provided below. The contests run for 9 months, from September 2026 until the beginning of June 2027. New problems are set each month, and contestants may submit their solutions until the beginning of the following month. The final results of the contest will be announced by August 2027 and in the upcoming KöMaL issue in September 2027. Prizes will be presented next autumn at the KöMaL Youth Conference.
We announce contests in mathematics, physics and informatics, altogether in 20 categories with different difficulties. Each contest lasts for 9 months, from September 2025 until the beginning of June 2026; new problems are posted in every month from September to May, and solutions can be submitted before early next month.
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?
