Number of Combinations
Due to different numbers of visually identical pieces in the two versions of the puzzle, they each have a different number of possible combinations. There are 60 tip pieces and 20 centres with 3 orientations, giving a theoretical maximum of 60!·20!·320 positions. This limit is not reached on either puzzle, due to reducing factors detailed below.
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Famous quotes containing the words number of, number and/or combinations:
“I am walking over hot coals suspended over a deep pit at the bottom of which are a large number of vipers baring their fangs.”
—John Major (b. 1943)
“Take away from the courts, if it could be taken away, the power to issue injunctions in labor disputes, and it would create a privileged class among the laborers and save the lawless among their number from a most needful remedy available to all men for the protection of their business interests against unlawful invasion.... The secondary boycott is an instrument of tyranny, and ought not to be made legitimate.”
—William Howard Taft (1857–1930)
“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)