# Rubik's cube question

**URL:** https://boards.straightdope.com/t/rubiks-cube-question/375294
**Category:** Factual Questions
**Created:** [October 4, 2006, 7:17pm UTC](https://boards.straightdope.com/t/rubiks-cube-question/375294 "2006-10-04T19:17:25Z")
**Posts on this page:** 2
**Page:** 2

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### Author: ![Fish](https://avatars.discourse-cdn.com/v4/letter/f/bc8723/32.png) [@Fish](https://boards.straightdope.com/u/Fish)
#### Post date: [October 5, 2006, 6:56am UTC](https://boards.straightdope.com/t/rubiks-cube-question/375294/21 "2006-10-05T06:56:34Z")

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> [@garygnu](#):
>
> To have three adjoining, visible sides solved, all the corner cubelets have to be in the correct position, there’s no way around this.

I don’t remember making this assumption in the OP, but it’s this kind of answer which is most useful: not the statistical number of mathematically possible configurations, but the number of actual combinations one can make with an actual cube.

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### Author: ![Omphaloskeptic](https://avatars.discourse-cdn.com/v4/letter/o/bcef8e/32.png) [@Omphaloskeptic](https://boards.straightdope.com/u/Omphaloskeptic)
#### Post date: [October 5, 2006, 9:11pm UTC](https://boards.straightdope.com/t/rubiks-cube-question/375294/22 "2006-10-05T21:11:50Z")

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> [@Fish](#):
>
> I don’t remember making this assumption in the OP, but it’s this kind of answer which is most useful: not the statistical number of mathematically possible configurations, but the number of actual combinations one can make with an actual cube.

Well, most of the answers (including mine, **CJJ** \*'s, and **CalMeacham** ’s) involve actual cubes. I’m not sure quite what the “statistical number of mathematically possible configurations” is supposed to mean; it sounds like you think we’re making estimates or bounds. But my answer of “96” is not a bound, it’s the actual answer (assuming **CJJ** \* and I have calculated correctly). I could list them all, and manipulate a real cube into any of them without any disassembly.

The difficulty is that the number of actual combinations you can make that look the same on the three front faces _depends on what you want the faces to look like_. There are exactly 96 cube states that look solved on the front faces; these are due entirely to moving edges about (since, as **garygnu** also points out, the corner positions can all be deduced).

For some front-face appeances (like the three I described earlier) there are more than 96 cube states that look the same. For the first case, for example, there are six possible corner states and so 6\*96=576 possible states for the cube.

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