I guess that could arise in several ways:
- The conjecture is worded in a way that is a puzzle that is difficult to solve.
- The hidden rule makes it difficult to determine whether a board is green or red, or to construct green or red boards that meet certain properties (or to find green or red examples at all).
In the latter case, we might discover it quite quickly when the rule master struggles with labelling grey boards. In the former case, maybe the conjecturer would have to simplify their statements first.
There are countless ways to embed difficult, arcane or computationally expensive problems into rule/conjecture statements.
One example would be to say that the valid koans are optimal solutions to a particular set of board coloring problems.