Consider the sequence of 9 non zero distinct digits arranged in a 3 by 3 grid , like
547
398
162
Clearly there are 9! (=362880) ways to do it.
If we demand that the consecutive numbers are next-door neighbours
( horizontally or vertically) like
167
258
349
then the number is significantly lower, say N.

Find N & provide your reasoning.

(In reply to computer verification by Charlie)

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Posted by Richard Scot on 2022-10-28 02:38:07