tl;dr:
1. Solve some equations
2. Notice that we simply need to maximize dot product of given vector and vector of our choosing

Full writeup: https://github.com/p4-team/ctf/tree/master/2017-11-09-defcamp-final/adversarial

Original writeup (https://github.com/p4-team/ctf/tree/master/2017-11-09-defcamp-final/adversarial).