Although there is no explicit rule against using a "no hardcoding" rule to "fix" a fixed output challenge,
A challenge must have objective validity criteria.
This means that "hardcoding" cannot form part of the specification wording unless the meaning of "hardcoding" can also be objectively defined. Unless we have a separate Meta discussion to agree on a default meaning for the word, this means that the challenge specification itself must contain a definition.
Although it may seem perfectly obvious what the word means, different people may draw the line through the grey areas in different places, particularly when it affects which approaches are valid in competition.