Five-digit number

Anna thinks of a five-digit number not divisible by three or four. If he increments each digit by one, it gets a five-digit number 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:

n1=65431 a1=76542 b1=54320  n2=76531 a2=87642 b2=65420  n3=76543 a3=87654 b3=65432  n4=86431 a4=97542 b4=75320  n5=87631 a5=98742 b5=76520  n6=87643 a6=98754 b6=76532  n=6

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