UpdateProblem writes the few settings the contest keeps for a problem of its own; anything else about the problem is edited in the archive instead. Reordering happens here too and there is no separate move method: writing an index moves the problem to that position and the problems it passes shift to keep the numbering contiguous, while an index of zero or beyond the last position puts the problem at the end. Only fields named in the patch are written, an empty patch writes all of them, and a finalized contest rejects the call.