# Skewb Star Special Challenge/Competition, with Special Prize

SKEWB STAR
Special challenge/competition 24 October 2018
by Peter Tchamitch
www.petertchamitch.se

Question 1:
How many solutions are there to this puzzle?--in other words, in how many different ways
is it possible to physically orientate a solved octahedron and a solved cube/skewb in relation
to each other?

Question 2:
How many color-matchings (please see definition below) are there in total, in other words
what is the sum of all the various color-matching values for all the various solutions?
A “color-matching” is an instance of one of the sides of an octahedron-pyramid having the
same color as the side of the cube/skewb under the pyramid (in a solved Skewb Star,
obviously)

Before proceeding: just to be absolutely clear, the competition relates to a standard Skewb
Star with a 6-color cube/skewb combined with an 8-color octahedron where all six of the
colors on the cube are also to be found on the octahedron

As far as I can tell there is nothing anywhere about there being multiple solutions to this
puzzle, let alone about what properties these solutions might have, so the whole problem is
unknown and brand new; of course I can´t be absolutely sure that there isn´t something
somewhere about this, but if there is I certainly don´t know about it.

The sender of the first correct*** answers to Questions 1 and 2 will receive a custom-made
Skewb Star Xtreme and a custom-made Wolf Tooth Xtreme as pictured on the Extra Bonus
Challenge page; the easiest thing would be to Google "Skewb Star Extra Bonus Challenge":
the top search result will bring you directly to this page. These hybrids are the only such cubes in the world.
Please note that they are not for sale nor should they be sold to anyone. The winner will also have his/her
name published on this website. Please send competition entries to petertchamitch@hotmail.com

***
I´m completely certain about the solutions that I´ve found, and virtually certain that I´ve
found all the solutions that are possible--should anyone come up with some new ones I
would be extremely interested in that discovery!
Finally, it is interesting to observe that if one rearranges the colors on the octahedron, the
answer to Question 2 remains the same (and Question 1, obviously) even though the
individual color-matching values for the individual solutions are completely different (i.e.
not just the old values rearranged)--if anyone can come up with counter-examples I would
be extremely interested in that discovery also!