Explanation
This page simulates the top half (3 faces) of a cube like the one in this picture:
It is one of the more infuriating puzzles in my collection, as I haven't as yet found any way of systematically solving it. My usual approach is to search for combinations of moves that move a few facets whilst leaving most of the puzzle unchanged. In this cube short sequences that move only a few pieces seem very ellusive, especially then trying to position the diagonal elements. I wrote this tool to help me search more efficiently.
I have recently updated the colours to emphasise that the two sets of diagonal pieces are totally independent. No combination of operations will swap a light diagonal piece with a dark one.
To operate press the keys described below (you may need to click on the picture to give it the input focus). The number display is a debugging feature to help understand the javascript behind this page.
Equations
Use this section to enter equations and assign them to keys.
Equation:
Keys
a / A rotate corner A clockwise / anti-clockwise.
b / B rotate corner B clockwise / anti-clockwise.
c / C rotate corner C clockwise / anti-clockwise.
d / D rotate corner D clockwise / anti-clockwise.
x / X rotate the whole cube about the North-South axis.
y / Y rotate the whole cube about the East-West axis.
z / Z rotate the whole cube clockwise / anti-clockwise.
z / Z rotate the whole cube clockwise / anti-clockwise.
ALT-A focus on all elements.
ALT-D focus just on the diagonal elements.
ALT-E focus just on the edge elements.
ALT-N toggle number display.
ALT-P toggle "plan" view.
ALT-R reset.
User defined keys
these will appear here
Equations explained
In this application operations on the cube are mapped to letters, so for instance pressing 'A' rotates one of the corners through 120 degrees. This is fine for short sequences but if you would like to generate longer sequences by repeating shorter sequences you can use the equations feature. Type the equation you wish to apply into the edit box and press the "Apply" button.
There are 4 syntactical elements to equations.
- A sequence of letters forms the basic atomic element, for instance "ABCD" will perform operation 'A' followed by 'B' followed by 'C' followed by 'D'.
- The exponentiation operator '^' will repeat the previous sequence a number of times, so, for instance "ABCD^4" will repeat the sequence "ABCD" four times. Note the operator binds to the complete sequence, not just the 'D'.
- The multiplication operator, '.' combines two sequences, so "AB.CD" will perform "AB" followed by "CD", which is the same as "ABCD". It is more useful when the sequences being combined contain operators of their own. For instance "ABC^3.cba^3" will perform "ABC" three times, then "cba" three times. This actually does nothing as "cba" is the inverse of "ABC". If in the exponentiation section you really wanted "ABCDDDD" you could have entered "ABC.D^4".
- Brackets: These are used to combine a number of other operations into an atomic element that can then be combined with other elements using the operators above. For instance "(ABC^3.cba^3)^12" will repeat "ABC^3.cba^3" twelve times.
Saving an equation
To save an equation enter text in the format "<letter>=<equation>". This will asign the equation to the letter. You can then type that letter to apply the equation, or use that letter in other equations. For instance typing "f=abAB" will assign the equation "abAB" to the letter 'f'. Then typing "f^4" will be the same as "abAB^4".
Some examples
I wrote this application to help me find combinations of moves that have simple results that I can combine into a solution. Here are a few I have found, click on the ">" button to try them out.
abcd^5
Rotates three of the edges around the top face, inverting 2 of them in the process.
BADC^5.abcd^5
"BADC^5" is the mirror image of "abcd^5". Combining the two results in a swapping and flipping of two pairs of the top 4 edges.
AB^35 ab^35
Move centre squares around the cube.
ACac AC^3 (AC^3.rr)^2 (AC^3.rr)^3 (acAc)^3
Operate on the set of three elements forming the diagonal of a face as if they were a single piece.
(BADC^5.a.abcd^5)^5 (AC^3.r)^6 (acAc)^3.(DBdB)^3
Not much use in solving the puzzle but produce interesting patterns.