I am slightly confused by your question. What do you mean "a pair of problems"?Originally Posted bymong sody

Thus, far I did is this,

Let be the number of contestants. Let be the number of contestants which solved exactly questions. Thus,

But nobody solved all six thus, . Thus we have that,

.

Now, I am trying to determine which one of x's has to be greater then , but I do not understand what you mean?