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There are ways to make impossible puzzles also.
Slight correction; there are ways to set up the balls so that there is more than one correct solution. You do this by setting up an outer ring of balls such a way that they prevent the guesser from learning any information about the remaining ball, which is then constrained to between 2 and 4 positions, if memory serves. This is relatively easy in a 5-ball game, but the patern is unique (give or take rotations and translations) in a 4-ball game.
My house rule is that the code master may choose to set up such a position if they wish, but that the score of the guesser is divided by the number of possible solutions once they have found the possible locations for the remaining ball.