DNSimple Infrastructure Instability Issue
dnsimple.statuspage.io4 pointsby ilikepi0 comments
x x x x x
x x x x x
x x . o o
o o o o o
o o o o o
For any given configuration of the x-subset, you flip and reverse that to get the configuration of the o-subset. There are 2^12 possible configurations of the x-subset. Since there are two possible values of the center square, that gives us 2^13 configurations of two-subset radial symmetry. I believe rotating 90 or 180 degrees simply produces another configuration that has already been accounted for. a a a B B
a a B B B
D a . c B
D D D c c
D D c c c
however, I think these would all be special cases of two-subset radial symmetry. If I pick a random configuration for the a-partition and apply it to the other subsets, it matches a configuration that would appear in the two-subset group: a a a B B X X o B B X X o o X
a a B B B o X B B B o X X X X
D a . c B => D X . c B => o X . X o
D D D c c D D D c c X X X X o
D D c c c D D c c c X o o X X
So between mirror symmetry and radial symmetry we have: 2^17 + 2^13 = 139,264. There are a total of 2^25 = 33,554,432 configurations irrespective of symmetry, so that's 17/4096 or roughly 0.415% that are symmetric...a bit more than 1/256.
* https://www.youtube.com/watch?v=fcvPifFSUL0&t=32m29s
* https://www.youtube.com/watch?v=fcvPifFSUL0&t=47m12s