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Anecdotal, not empirical, but: Collatz conjecture (easy to state, unsolved), and "return the last digit of this huge, incompressible number" (big KC, trivial)
Where does the number come from? If it's arbitrary, then it needs to be hardcoded in both the spec and the solution (thus similar KC). If it's algorithmically generated, the algorithm must be included in both, too. If it's a known constant, it can be abstracted away (low KC)
