Wetten, dass..? vom 5. November

I invented a new scrambler/notation for the megaminx, much easier and faster to use than the previous WCA one (from which I stole the basic image). By now the WCA has adopted it. Look at the pictures below. Hold the megaminx with your left hand, the blue corner-edge-corner triple with thumb and index finger, the other fingers help hold the rest of the puzzle. The right hand makes the moves. An R turn moves the whole puzzle except the left layer, a D turn moves the whole puzzle except the top layer, a U turn moves the top layer.

Now an example scramble:

    R-- D++ R++ D-- R++ D-- R++ D++ R-- D-- U'
    R++ D-- R++ D-- R-- D++ R-- D-- R-- D-- U'
    R++ D++ R-- D++ R++ D++ R++ D++ R-- D++ U
    R-- D-- R++ D++ R++ D++ R-- D++ R++ D++ U
    R-- D++ R++ D-- R++ D-- R++ D++ R++ D++ U
    R++ D++ R++ D++ R-- D-- R-- D-- R-- D-- U'
    R-- D++ R-- D++ R++ D++ R++ D++ R++ D++ U

Notice that "++" means two-fifth turns clockwise (in the direction of the arrow) and "--" means two-fifth turns counterclockwise (against the direction of the arrow). It's intentional that there are only two-fifth turns and no one-fifth turns, I believe this improves the scramble quality.

If you want to discuss this scrambler/notation, please visit the WCA forum thread or the speedsolving.com forum thread. This page describes the result of my own experiments as well as feedback from others. If further improvements turn up, you'll find them on this page here.

If you're able to analyze the quality of scrambles like I suggested early in the WCA thread, your results would be very welcome.

Here's one analysis, my computation (source code) of the probabilities of where each center will end up:

          DLB   DLF   DRB   URF   ULF   B     F     U     URB   DRF   ULB   D       min   max      sum
     pink 8.329 8.329 8.326 8.338 8.341 8.327 8.340 8.347 8.338 8.327 8.340 8.320   8.320-8.347 => 100.000
    blue2 8.329 8.329 8.326 8.338 8.341 8.327 8.340 8.347 8.338 8.327 8.340 8.320   8.320-8.347 => 100.000
   orange 8.347 8.347 8.329 8.320 8.338 8.336 8.331 8.321 8.320 8.336 8.331 8.346   8.320-8.347 => 100.000
   purple 8.338 8.338 8.341 8.329 8.326 8.340 8.327 8.320 8.329 8.340 8.327 8.347   8.320-8.347 => 100.000
turquoise 8.320 8.320 8.338 8.347 8.329 8.331 8.336 8.346 8.347 8.331 8.336 8.321   8.320-8.347 => 100.000
   green2 8.340 8.340 8.328 8.327 8.339 8.332 8.334 8.331 8.327 8.332 8.334 8.336   8.327-8.340 => 100.000
    green 8.327 8.327 8.339 8.340 8.328 8.334 8.332 8.336 8.340 8.334 8.332 8.331   8.327-8.340 => 100.000
    white 8.326 8.326 8.347 8.341 8.320 8.339 8.328 8.329 8.341 8.339 8.328 8.338   8.320-8.347 => 100.000
     blue 8.338 8.338 8.341 8.329 8.326 8.340 8.327 8.320 8.329 8.340 8.327 8.347   8.320-8.347 => 100.000
      red 8.340 8.340 8.328 8.327 8.339 8.332 8.334 8.331 8.327 8.332 8.334 8.336   8.327-8.340 => 100.000
    brown 8.327 8.327 8.339 8.340 8.328 8.334 8.332 8.336 8.340 8.334 8.332 8.331   8.327-8.340 => 100.000
   yellow 8.341 8.341 8.320 8.326 8.347 8.328 8.339 8.338 8.326 8.328 8.339 8.329   8.320-8.347 => 100.000

Stefan Pochmann
Last modified: November 02 2009, 17:23:36