Gold is first 4 teams

First two people got more then 0 correct predictions because: "four sets of gold medals, four sets of silver medals, and four sets of bronze medals are awarded"

I had WA13 on FreePascal with TStringList.IndexOf() method.
Try write IndexOf (or what you use) "manually". Perhaps this is due to hidden features of  string conversion/comparison.

I have no idea what is the test #5, but I kept getting it because of a mistake like this:
find(v.begin(), v.begin()+4, key) != v.end().
                                       ^^^ must be v.begin()+4

Nobody said that they are the same university. You just don't understand the sample.

maximum number of true predictions can be 0. Vadik will pay 5 dollars to all, if there were no any true predictions.