Parity or: How I Learned to Stop Worrying and Love the 4×4

After painstakingly modding my Shengshou v4s a couple months ago (mod post coming soon), my interest in 4x4s has waxed and waned. On the one hand, I find it a welcome and more challenging distraction from 3x3s; on the other hand, those damn parity algorithms!?! I have finally committed them to muscle memory and am now trotting along at a 2:20 average using the Yau variation of the reduction method. (For more on Yau, and especially the cross-on-right variation that I find easier, check out Cyoubx’ really good Yau intro video.)

For months, parity was my albatross. I finally conquered it, so to speak, not only by finding and learning algorithms that worked for me, but also my learning about the root causes of parity. This was by far my deepest dive into puzzle theory and its associated patois. Keep reading past the jump for much more on the types of cube parity, what causes each, and, most importantly, what we really mean when we sloppily say that a cube has “parity.”

PARITY ALGORITHMS

If you’re just here for the algorithms, look no further:

OLL Parity
4x4-oll-parity

[1] Rw U2 x Rw U2 Rw U2 Rw’ U2 Lw U2
Rw’ U2 Rw U2 Rw’ U2 Rw’

[2] (Rw Lw) U2 Lw’ U2 Rw’ U2′ x’ U2 Rw’ U2′ Rw U2 Rw’ U2′ Rw2 U2

PLL Parity
4x4-pll-parity

Uw2 Rw2 U2 r2 U2 Rw2 Uw2

Here’s a (now muted due to copyright claims) video showing each:

(music: Bob Dylan, “Subterranean Homesick Blues; cubes: Konsta+Florian modded Shengshou v4s with Cube Specialists Bright+ modded stickers)

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43 quintillion possibilities

Short post today, my first from the WordPress iPad app. Sometimes you see something done so well, so elegantly, so cleverly that you can share it with little commentary. Such is the case with Kenneth’s (RedKB) “Why is the Rubik’s Cube So Hard?!?!!” video below. The answer, of course, is that there are 43 quintillion possible cubie combinations on a 3×3 cube, only one of which is “solved.” But 43 quintillion is impossibly hard to understand. Until now:

Kenneth also has a follow up episode on the probabilities surrounding a 7×7, with conclusions that are hard to believe.

This makes me want to do a post on the math behind 43 quintillion. Soon….