[munchler]

It's not unlikely at all. We're talking about numbering four tiles in a square, right? There are only two natural ways to do it for anyone who writes in a left-to-right, top-to-bottom language:

    1 2

    3 4

Or (less likely):

    1 3

    2 4

In binary, note that both of these patterns naturally assign one bit to left-right, and the other to up-down, which is a very desirable outcome. E.g.:

    00   01  (0x row)

    10   11  (1x row)

   (x0  (x1
   col) col)