How many states?

Borodog · #1 01-08-2007, 12:23 PM

This question is in regards to this post.

Cliffs notes: Mother-in-law gave me a "Soduku cube", in which the object is to get the numerals 1-9 to appear on every face exactly once. There appears to be one "meta-solved" state in which the numerals appear on the faces in numerical order:

and many "simply" solved states in which all 9 numerals appear on every face, but not in the correct order (as in my photo in the above thread). I hit on one of the "simply" solved states by accident.

The question has become, how many simply solved states are there?

kinghippo423 · #2 01-10-2007, 02:51 AM

Same as the Rubik's Cube : 1

Siegmund · #3 01-11-2007, 05:13 AM

A simulation, based on the descriptions of the cube Borodog has posted, says that a randomly twisted cube lands in a "simply solved" state once in 30 or 40 million twists.

I had thought that the odds of it might be just one in several hundred thousand, but my intuition was a bit off - or, of course, Borodog hid something on the other three faces of the cube

vhawk01 · #4 01-12-2007, 02:38 AM

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Same as the Rubik's Cube : 1

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Wow, good guess, and so close too.

southerndog · #5 01-12-2007, 05:23 AM

12

Dromar · #6 01-12-2007, 09:13 PM

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12

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I agree with this. There are 12 "simple" solutions, one of which is the "metasolved" position.

BogusPomp · #7 01-13-2007, 12:55 AM

I've been thinking about his a little.... a question, since there are 4 different cubes labeled 6/4, aren't there at least 4! or 24 different 'meta-solved' solutions. As for simple solutions, still churning on that one. just as curious as you.

Misfire · #8 01-14-2007, 01:55 AM

Is it considered solved if the numbers are upsidedown? Even if so, I'm sure there's fewer than we'd imagine. The 5s are stationary in the center, and the corners are fixed with their three numbers. I have no idea how to do the math, but I'd be suprised if there were more than a handful of variations.