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 Post subject: My Gear Shift solution (with diagramm)Posted: Fri Oct 07, 2011 5:23 am

Joined: Mon Feb 06, 2006 12:52 am
After watching Bram’s Tutorial on the Gear Shift solution I decided to post what I had come up with.

Or in other words just how I approached the puzzle.

When I was messing with the cube after some time I ran into the case where one small gear was turned and the rest solved. After a while of doing just some random stuff I came to the conclusion that I should try to get only the small gears into their right orientations regardless of what happens to the large gears. So I came up with the diagram below.

First you need to notice that all small gears turn the same direction. So the circles in the diagram should not be seen as gears being intersected in pairs. The circles are only the small gears on the gear shift. They can be operated in pairs of two. There are 6 pairs. Top, bottom, left, right and two diagonals. Another way to see it is this: The gears on the puzzle can be separated along 3 axis and each axis gives two halves.

What you do to solve only one type of corners first (in my example the small ones) is first to get three of the corners correct. This is really easy. IF you find one of the corners to be wrong you just hold the cube so it matches with the first picture in my diagram. To explain this: The circles with a vertical line are correct. The upper right circle is wrong. The line is one fourth off. Just hold the cube so the wrong corner is top right when you look at it in front of the diagram. Just imagine the third dimension wouldn’t be there and all (small) gears are just there (in some plane).

The only thing you need to do is separate the cube’s halves in a way the orange boxes tell you and perform the steps. To do this you need to note that in my diagram it says 1/4 , 1/8 , 1/16 … Obviously these angles don’t apply to the cube 1:1. But the basic idea is to bring a gear that is off by 4 teeth, even though 4 teeth aren’t even one fourth of a rotation, down to being two teeth off. Just divide the number by two always and get closer to the correct orientation.

When you are done with the diagram you should have all gears of one kind correct. The next question is how do you get the others right. Going through the diagram again for the other kind will mess up the first again right? Not if you keep this in mind: You can rotate the solved gears around exactly by multiples of full rotations. So they stay right, but since the gears have different number of teeth it will leave the other kind of gears turned by some amount of teeth/ some angle.
So yes, you just repeat the diagram always turning the solved gears fully around. Just make sure you interpret the lines not by exactly the fractions I put there but more basically. In the end the diagonal gears (last pic) just need to be off by the same amount of teeth.

Attachment:

diagramm gear shift.JPG [ 55.4 KiB | Viewed 660 times ]

Now a couple of things:
1st: A small gear that is off by one tooth can’t be gotten closer to the correct orientation because one tooth can’t be divided by two, right? Correct. But one tooth means four teeth the other direction. So just get it two out of these four into that direction. Than one more tooth for the next graph in the diagram. Then you’re done.
2nd: In this whole description I solve the small gears first. It both works but I guess solving the large ones is easier because for the second step of solving the small ones you only have five different orientations. If you solve the small ones first you have eight different orientations for the large ones. (Because the small ones can do eight complete rotations before everything is the same again, whereas the big ones do only five full rotations in that time.)

But both ways work and are fun.

So now the question remains how much different this is from Bram’s solution. I guess it takes even longer but isn’t much different. If you solve one kind of gears and then get three gears of the other type correct easily, I guess you could have done those along from the start which is what Bram did. I also guess that the moves he does to solve the last wrong orientated gear are about the same as those in the diagram.
I just still thought I could post this because I feel that it gives some insight in why the cube is solved the way it is rather than just doing what you learned and memorizing it. I wouldn’t understand how and why Bram did what he did when I watched the vid the first time. I did that only after I figured my own solution but still I thought maybe someone who only watched the vid doesn’t fully know what he is doing.
But again the vid is probably the quickest way to get there without any superfluous moves and separations that my solution has.

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Life is simple.
eat. sleep. train. repeat.

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 Post subject: Re: My Gear Shift solution (with diagramm)Posted: Fri Oct 07, 2011 6:02 am

Joined: Mon Feb 06, 2006 12:52 am
URGH! I just noticed a little "flaw" in my diagram. Not really something that is wrong but superflous.
In the second picture it is enough to just turn the top two circles by 1/8 leaving one diagonal solved an one diagonal off by 1/8.
For some reason I was myself always wondering why I needed to turn two halves there. I was probably too obsessed with getting it closer and closer and reducing the fraction.
It's better to turn just one halve and leave one diagonal solved in that step. Sorry I didn't notice earlier.

_________________
Life is simple.
eat. sleep. train. repeat.

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