The Answer to the Question
is below this banner.
Here's the Solution to this Question
Let the total number of participants be (if the proof is trivial). Denote
the set of people who missed the first problem by
the set of people who missed the second by
and the set who missed the third by
We know that and
We also know, that
The set of people who solved all three problems is the complement of (the set who missed at least one problem), so it has size
Therefore at least 25% of the participants solved all three problems.