... it's driving me nuts. Trouble is, it's not a well-defined question. So i guess I'm just asking for an educated opinion.

In 1968, a friend and I dropped in on a mutual friend. He has just bought a Rubik's cube, and was very cross. He said he had spent all of his spare time that weekend trying to figure it out, and "I'm no closer to it now than I was when I started." And he tossed it onto the coffee table.

I picked it up and started randomly moving the faces, admiring the pretty colors and enjoying the tactile sensations. I had never seen one before.

We chatted casually. I wasn't trying to solve it, I'm not fond of puzzles. Finally I sort of forgot what I was doing, caught up in conversation, but I kept idly moving the faces with my fingers. It felt cool, and made soft clicking noises.

Suddenly our host's face froze, and he literally turned pale! Staring at me, he demanded, "How did you do that?" I looked down. The puzzle was solved.

So: Here's my question.

The astronomer Hoyle has said:

quote:

If our ... subject were to make one random move every second, it would take him on average three hundred times the age of the earth, 1,350 billion years, to solve the cube. The chance against each move producing perfect colour matching for all the cube's faces is about 50,000,000,000,000,000,000 to 1.

Granted our host's moves were purposive. Yet isn't if very highly unlikely that I would yield a solution in less than an hour's idle toying with the damn thing?

What are the odds?

I think that Hoyle is wrong. The way probability works it might well take several billion random moves to produce a solution; but the solution is not likely to take place at the last random move in the billions of moves. In other words the probability of solving the puzzle would only mean that the likelihood of producing more than one solution in that number of attempts is highly improbable. Look at the powerball lottery winners, sometimes there is no winner sometimes several, for Hoyle statistics to be dependable requires attributing a capability for memory in an inanimate object. In the process of tossing a coin the probability is that there will be as many heads as tails, but it is quite likely that in ten tosses there could well be ten heads, for instance. The math ratio is most accurate as the number of repetiotions increases. I think it would be said to increase asymptotically.

That said, it wouldn't surprise me at all, if you, Babs, were to solve it the first time in nothing flat.

I do not want to be a spoil sport, but I wonder how the cubes are scrambled. Are they all scrambled the same way, or are some scrambled more or less than others? Maybe the particular cube was not scrambled that much. Anyway, babthrower did say that the cube had been worked on = scrambled by her friend. Yet, this does not definitely lower the possibility of solution, since any number of moves by any number of persons are random. Babthrower, I agree that this one can be a brain scrambler. My gut feeling is that the cube was originally scrambled in a direction towards one, and your friend and you both effectively unscrambled it in a direction away from the one unscrambling it, or vice versa. How's that for a strong factor increasing the likelihood of solution? Translation: there must be at least one factor which increases the likelihood of solution, thereby causing us to chuck the thought that every cube's randomness is equal either from the store or from how it is subsequently handled.

I am reminded of how when one person tries to open a bottle but declares that he/she cannot do it, nevertheless, the first person who also had tried goes ahead to try again, picking up where the second person gave up, and voila, the bottle opens.

Now, if anyone knows why some candy stores seem to have more lottery/lotto winners than others. . . .

quote:

Now, if anyone knows why some candy stores seem to have more lottery/lotto winners than others. . . .

The widespread misunderstanding of randomness and probability is the reason some people keep on gambling despite the odds against winning. Gamblers often reason: "I've already pulled this lever five hundred times, so - odds are that I'm DUE to hit a jackpot". When the poor slob runs out of money and goes home, the next dilettante puts in her four or five dollars and wins a bundle. Every attempt has the exact same odds, it is only "probability" never "certainty". Odds of fifty to one doesn't mean a winner every fifty tries, it could mean 3 winners in the 145th 148th and 150th try - or even none until the 200th.

frankvan: I used to play those one-armed bandits in a particular casino each trip to Atlantic City. I walked in a poor slob expecting to kiss away my few extra dollars, and I walked out a broke and slightly depressed poor slob. Then, I learned to move to a nearby machine so that I could see that my stashes were usually going to sweet, smiling, elderly ladies. As a result, I would go home broke but not slightly depressed. Finally, I stopped going to Atlantic City so that I could be a sweet, smiling, baby boomer with a few dollars in the bank.

Rubik's cube is not random. There are adjacencies and key pieces. It is unlikely but possible for you to sit and resolve it while fiddling.

I mean, seriously, weren't you looking at it at all?

Babs, you had us going there for a while! Ernő Rubik invented the puzzle in 1974, while it wasn't marked as a toy until 1980. So given the 1968 time frame of your story, it's pure confabulation -- you are to be congratulated for a brilliant bit of tomfoolery.

Given that the number of permutations of the cube is around 4x10¹⁹, your account of randomly solving the puzzle would suggest that the original scrambled position was just a small number of moves away from the original solved state, whose reversal you somehow stumbled upon -- that would at least put it within the realm of plausibility.

There is a skeptical principle that when considering an apparently highly improbable event such as you describe, one must consider the more likely alternative of a hoax. I think this nicely illustrates the point.

Now 'fess up.

Your research is flawed. This



-------happen7ed in7 198 - (1969 at the latest) which is the year I graduated university. In September
1969 9 I moved to B.C. and have only been back three twice since -- once in 1972 and twice in 1976. I haven't seen tThe young man who owned the Rubik cube since 1969.

Sooy, my keyboard is messed up -- the brank new cordless!

Babs, your man should have patented the cube he had. He'd have been the millionaire instead of Rubik. The Rubik's cube official online site gives the date of invention as 1974, of the patent as 1975 and of the first 'test batch' production for the market as 1977.

Cube

Well, I have a 'loaner' keyboard and the answer to the poser.

It had to have been not a Rubik's cube, but a Soma cube. I got the site by googling "Rubik cube invented 1969".

quote:

The SOMA cube was invented by Piet Hein, a Danish poet, dreamer, mathematician and genius; way back in 1936. The puzzle did not become popular in the 'States until 1969 when Parker Bros. packed and shipped it as the "3-D answer to Tan-Grams".

You can see a picture of the cube here.

And this also makes my quesion obsolete. Since there are "many more" than one solution to Soma, who knows what the odds were against my solving it by some random toying with it as we three discussed all sorts of neat stuff.

And the same site answers Fred's question.

quote:

Sadly, the disco-erazoic Soma Cube was smothered away into extinction by another puzzle during the pre-rappazoic period. I'm not knocking the Rubik's cube, but it has only ONE solution. SOMA offers many more...

And since the game Soma was not the one to which Hoyle referred in his words that I quoted, not only who knows, but who cares?

But I'm sorry I jumped to the conclusion that the cube game I played with was Rubik's cube. It sent you guys off on a wild goose chase.

But I'm glad about something else: I don't have to get all spooky about something that I once did against freakishly impossible odds!

Heck, what would have been next?
Playing number games with ancient texts, trying to get at hidden secrets of the universe?

I'm happy to report that Soma Cubes are alive and well and still available -- I have two different versions of the puzzle purchased in recent years.

Not only are there many ways to assemble the pieces into a cube, there are a variety of puzzles based on putting the pieces together to form many different shapes.

And it's not all that difficult to fiddle around with the pieces to find a solution -- unlike Rubik's Cube.

And come to think of it, I first played with the Soma Cube around 1969 (actually I remember it as 1968, even though it wasn't marketed until 1969).

I'm glad to know that -- despite our faulty memories -- none of us have completely lost our minds.

The Rubik's cube is not that difficult, once you learn a few moves. It is solved, not one face at a time, but one level at a time.

There are counltless permutations, but only a few different last-level configurations from which to complete the cube. My best time is 1 minute, 22 seconds.

I remember doing the Soma cube when I was about 6.

Oh, I almost forgot, Perf, I must apologize for the statement I made about your research being flawed. It was my memory of the event that was flawed.

It's kind of interesting, in a way. I was just reading an article on memory, and it seems that we may reconstruct memories, each time we visualize the event, depending on the context in which we recall it. And it may be the 'edited' version that we later recall, not the pristine memory.

Clearly I combined memories of the nine-faced cube I handled in 1969 with seeing others use a Rubik cube years later. Some overlay happened here.

Makes you wonder about court evidence, where the witness has been 'sandpapered' quite a bit before he/she gives evidence.

By the way, Kendor, that sounds pretty impressive!

I may have been right: I wrote ". . . chuck the thought that every cube's randomness is equal either from the store or from how it is subsequently handled." The cube was of a different variety, all right.