Duck Contest
Duck Research
Given $k \in \mathbb{Z}_{>0}$, find
$$\lim_{n \to \infty} \frac{1}{n^{k+1}} \max_{\pi} \sum_{i=0}^{2n} |\pi(i) - i|^k,$$
where the maximum is taken over all permutations
$$\pi : {0, 1, 2, \ldots, 2n} \to {0, 1, 2, \ldots, 2n}.$$
Submit
The contest ended at 8:16 p.m. AEST on Thursday 2nd July. All submissions will be unofficial .
Announcement
1:57:40 p.m.
Late submissions have been enabled. This means that you can attempt the problems without your score contributing to the leaderboard. Thanks for participating!
Announcement
6:04:03 p.m.
The test data for P2 "Duck Waves" has been fixed, and all submissions for this problem will be rejudged soon.
Announcement
3:29:06 p.m.
We've increased the time & memory limit of the problem p3 "Duck Pond Gaps".
Announcement
12:44:45 p.m.
The website had an issue when we were configuring it that caused us to have to push the start back by an hour. Sorry!!!!