Do you know any nice tasks which require randomization to decrease complexity which are not well known (like: you are given given set of points, find a line with at least n/2 points <- this one is well known)? Such like 364D - Ghd. Unfortunately codeforces has only tag "probabilities", which is usually used for problems where we have to calculate probability of something. Every time when I come across this kind of problem I am impressed how cool it is, so maybe you want to impress me? :D