The latest on the Bonus Problem posted on 13 August 2019

The so-called Standard Method referred to in the Bonus Problem post of 13 August 2019 involves
finding the easiest or most convenient Skewb Star or Wolf Tooth solution, depending on how the
SSX or WTX respectively were scrambled, and then, unless the characteristic valleys between the
corners of the Skewb Xtreme just happen to be spontaneously solved, proceeding from there to the
other Skewb Star or Wolf Tooth solutions in an orderly manner until the valleys are observed to be
correct. No matter how orderly, this method still involves trial and error, and the Bonus Problem
was basically asking for a way to eliminate that somehow. The SSX and WTX have only one
solution each, by the way.

The natural thing would then be to study the stickers in the valleys to see if there were any clues or
recurring patterns there, and at first there didn´t seem to be any; however, it now seems that in fact
there are at least two such patterns and I was able to determine that once any solution to the Skewb
Star or Wolf Tooth portion of the SSX or WTX respectively is in place, a single application from the
correct direction of one rather long algorithm that takes about 30 seconds to execute solves the
valleys, most of the time: the rest of the time the patterns are nowhere to be seen and one first
has to apply once a slight variant of the algorithm, from any direction, to get the patterns to show up.

Just to be 100% clear, it is the positioning of the patterns that indicates from which direction the
single rather long algorithm should be executed; the algorithm itself, and the slight variant, are the
same as were devised way back, at the time the multiple solutions to the Skewb Star and Wolf Tooth
were discovered, to make it possible to efficiently alternate between these various solutions.

Needless to say, the improved system above is not at all in the same class as Jakub Stepo´s solutions
to the two Skewb Star Competition problems--please see my 29 August 2019 post--which are
authentic proofs: all I´ve done is to notice certain recurring patterns in the valley-stickers of the
Skewb Xtreme portion of the SSX and WTX, and I should have seen them a lot earlier because the
patterns in question are hiding in plain sight! It remains to be shown formally exactly why the
improved system described above works, and it cannot be ruled out, of course, that there are
completely different and even more efficient types of solutions waiting to be discovered.