I just had a really crazy, improbable, occurrence happen on my cube. I've been speedcubing for 11 years and have never once seen this happen until today.
I was idly solving my cube with hand scrambles, nothing unusual. I wasn't trying to go super fast, just trying to focus on my form with my triggers and making sure I was making good F2L decisions.
After solving an Xcross and the next pair I noticed that both of the other 2 pairs were solved, but the corners were flipped. Both corners had to flip the same direction and I used a BLD 3 corner flipper, flipping one corner from the U layer also, to solve them. After that I recognized the OLL, but then I noticed that all the pieces in the LL were correctly placed as well (!), but also only misoriented. Rather than do OLL and PLL I did my BLD algs to flip those pieces too!
The weird part about this scramble, and the thing I have never seen before until today, is that after solving the cross and the first two pairs, all the remaining pieces on the cube were in their proper places, only misoriented. I did not even need to AUF in order to ensure this, it had already happened!
The probability of having all the remaining pieces solved (but they may or may not be oriented correctly) after solving only the cross and two pairs is:
1 / [6!*6!/2] = 1 / 259200
A couple years back I estimated that I've probably done about 400,000 solves in my lifetime, so by today I might be around 450,000. The chance of me doing that many solves, and seeing this exactly once, is:
450000 * (1/259200) * (259199/259200)^449999 = 30.6% chance, which is of course a perfectly reasonable probability of occurrence.
Cool!
Chris
(mirrored g-perm)
