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:
“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)
“One may confidently assert that when thirty thousand men fight a pitched battle against an equal number of troops, there are about twenty thousand on each side with the pox.”
—Voltaire [François Marie Arouet] (1694–1778)
“Europe has a set of primary interests, which to us have none, or a very remote relation. Hence she must be engaged in frequent controversies, the causes of which are essentially foreign to our concerns. Hence, therefore, it must be unwise in us to implicate ourselves, by artificial ties, in the ordinary vicissitudes of her politics or the ordinary combinations and collisions of her friendships or enmities.”
—George Washington (1732–1799)