There are different ways of adding arbitrary additional conditions, but you need to be careful not to apply too strong additional condition which turns out to be contradictory. One safe way is to imagine having a triangle ACE, with B, P, and Q being the midpoints of AC, CE, and EA, respectively. If the positions of images A', B', and C' define only the intersection point of a focal plane with the line AC then the positions of images A', P', and E' define another point on the focal plane.
Please submit the solution to this problem via e-mail to physcs.cup@gmail.com. The next hint for the Problem 4 will be published at 13:00 GMT, 13th March 2022, together with the next updates of the intermediate results.