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:
“In view of the fact that the number of people living too long has risen catastrophically and still continues to rise.... Question: Must we live as long as modern medicine enables us to?... We control our entry into life, it is time we began to control our exit.”
—Max Frisch (1911–1991)
“I wonder love can have already set
In dreams, when we’ve not met
More times than I can number on one hand.”
—Philip Larkin (1922–1986)
“The more elevated a culture, the richer its language. The number of words and their combinations depends directly on a sum of conceptions and ideas; without the latter there can be no understandings, no definitions, and, as a result, no reason to enrich a language.”
—Anton Pavlovich Chekhov (1860–1904)