We designed this problem so that it's easy to create inputs and to check an output on our side, but it's hard on the teams' side.
We don't know how the teams actually solved this one. It is easy to make an educated guess about most of the inputs, but that would not be very precise. During the contest each team could submit solutions 24 times at most. Using the score information they could calculate the rank of their guess, which can be used to fine tune their guess to some extent.
All the inputs: