User blog comment:Kolmogrov142 Oracle Tuto X/Interesting combinatoric results in relation to large numbers./@comment-80.98.179.160-20180126111604/@comment-1605058-20180126194822

I think the point here is that this depends on whether we consider all the squares to be distinguishable from each other or not. For example, if we swap two white squares, does it count as a different rearrangement? If yes, then we do get 64! rearrangements. If not, only \(\binom{64}{32}\approx 1.8\cdot 10^{18}\).