Hi guys!a math question:

i've spent lots of hours trying to figure it out,so if it seems easy,i'm just dumb not lazy^^

anyhow:

i'm reading the artificial intelligence book by russel and norvig,where the 8 puzzle is described as the usual 3*3 board with 8 numbered tiles and an empty cell...

the authors claim that only 9!/2 states can be reached from a given initial state(wich means there are only 2 equivalence classes).well intuitively it seems

correct,but i can't figure out any satisfying proof.i know i just could use a few lines of code to calculate this,but the authors mentioned that so casually

that it seems like it's the result of a very simple deduction...so what am i missing?

by the way i posted that on mathoverflow,they closed it in less than 5 minutes.