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Those 3 letters are the only ones that can define 4 numbers in this way which is why it asks what will they do next month?
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If Z works then N works so there are not just 3 letters that work. The puzzle is broken.
Many security keypads are 4 rows of 3 columns where a T can also give 1320. The puzzle does not provide a unique solution.
Many security numeric pads are 2 columns of 5 or 6 where the puzzle is nonsense.
Not a turtle wax worthy puzzle.
Dale B. Dalrymple