Just a note, posting here because some people might have participated in something similar (if so, what were your impressions?):

...Unfortunately, at the all-Soviet [mathematics] Olympiads they failed to implement another idea, which A. N. Kolmogorov put forward more than once: to begin one of the days of the contest with a lecture on a previously unfamiliar, to the participants, topic and then offer several problems which would build on the ones considered during the lecture. (Such an experiment was successfully carried out only once […] in 1985 […] the lecture was on geometric probabilities.)

N.Vasilyev, A.A.Yegorov. Problems of All-Soviet mathematical olympiads. - Moscow, 1988. - p. 14 of 286.