Nearly twenty years ago Vladimir Arnol'd has published a collection of exercises which he called Trivium but many of which are not trivial at all. In the french version of this blog you can find most solutions. You are invited to contribute solutions if you wish. Exercises no. 27, 41, 51, 58, 68, 69, 70, 73, 74 are still unsolved here.

Since the answers are posted in comments not following the original order of Arnold's exercises, the best way to find a solution on that page is to use Ctrl+F and look for "no.54", for example. The numbering of the exercises follows this french version which I found on the web and can be slightly different to the english, russian or german version.