Number of Combinations
The Skewb Ultimate has 6 large "edge" pieces and 8 smaller corner pieces. Only even permutations of the larger pieces are possible, giving 6!/2 possible arrangements. Each of them has two possible orientations, although the orientation of the last piece is determined by the orientations of the other pieces, hence giving us a total of 25 possible orientations.
The positions of four of the smaller corner pieces depend on the positions of the other 4 corner pieces, and only even permutations of these positions are possible. Hence the number of arrangements of corner pieces is 4!/2. Each corner piece has 3 possible orientations, although the orientation of the last corner is determined by the orientations of the other corners, so the number of possible corner orientations is 37. However, the orientations of 4 of the corners plus the position of one of the other corners determines the positions of the remaining 3, so the total number of possible combinations of corners is only .
Therefore, the number of possible combinations is:
Read more about this topic: Skewb Ultimate
Famous quotes containing the words number of, number and/or combinations:
“If we remembered everything, we should on most occasions be as ill off as if we remembered nothing. It would take us as long to recall a space of time as it took the original time to elapse, and we should never get ahead with our thinking. All recollected times undergo, accordingly, what M. Ribot calls foreshortening; and this foreshortening is due to the omission of an enormous number of facts which filled them.”
—William James (1842–1910)
“... [woman suffrage] has made little difference beyond doubling the number of voters. There is no woman’s vote as such. They divide up just about as men do.”
—Alice Roosevelt Longworth (1884–1980)
“One way to think about play, is as the process of finding new combinations for known things—combinations that may yield new forms of expression, new inventions, new discoveries, and new solutions....It’s exactly what children’s play seems to be about and explains why so many people have come to think that children’s play is so important a part of childhood—and beyond.”
—Fred Rogers (20th century)