The problem stated was that the marker machine lies 1 out of 15 entries. The paper would contain an incorrect selection occasionally. So, yeah, it would require no one noticing during the act.
My preferred machine would be one that did not use integrated circuits, but was simple enough that the entire board and circuit was visible - with no software beyond the circuitry at all. You just need a very simple sensor and tally wheels that mechanically advance, like those used for measuring wheels etc. No need for memory. Keep automation to the absolute bare minimum.