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cube-permutations.html
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<!DOCTYPE html>
<html>
<head>
<title>1x2x3 Cube Permutations</title>
<link rel="shortcut icon" type="image/x-icon" href="favicon.ico">
<style>
body {background-color: #222; position: relative; left: 10px; width: 90vw; height: 90vh;}
a, h1, p, span {color: #fff; font-family: verdana;}
input {margin: 4px 0px; display: block;}
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<body>
<h1>1x2x3 Cube Permutations</h1>
<img src="https://mcnole25.github.io/images/1x2x3-rubiks-cube.png" height=368px>
<p>All possible scrambles of the 1x2x3 Rubik's cube. There are 48 permutations, and we can demonstrate how.</p>
<p>Consider just the top face of the puzzle. With only 180° turns, we can move the top, left, right, or bottom parts. To preserve orientation, let's say top and bottom moves are identical. This means the lower middle cubie will be in a fixed position.</p>
<p>For the 5 cubies from the top face, there are only 12 possible orientations. For the red/orange side, since one of them is in a fixed position, we get only 4 possibilities. Red/Red/Red, Red/Red/Orange, Orange/Red/Red, Orange/Red/Orange.</p>
<p>For certain arrangements, the pattern is different and it depends on the green/blue side. Orientation of the puzzle is disregarded, so all of these patterns are unique.</p>
<img src="https://mcnole25.github.io/images/1x2x3-labeled.png" height=368px>
<p>These are the steps to go from solved to your scramble. You can determine that the maximum steps required is 6. U = up, L = left, R = right, lr = left-right (or right-left).</p>
<p>Individual steps are inverses of each other. Read the steps backwards to go back to solved (example: UL requires the moves LU to solve).</p>
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