Five-digit number

Anna thinks of a five-digit number that is not divisible by three or four. If he increments each digit by one, it gets a five-digit number that is divisible by three. If he reduces each digit by one, he gets a five-digit number divisible by four. If it swaps any two digits, the number is lower. John claims there are more than five possibilities. Was he right?

Correct answer:

n =  6

Step-by-step explanation:

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