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:
“There is not to be found, in all history, any miracle attested by a sufficient number of men, of such unquestioned good sense, education, and learning, as to secure us against all delusion in themselves ... beyond all suspicion of any design to deceive others ... and at the same time attesting facts, performed in such a public manner, and in so celebrated a part of the world, as to render the detection unavoidable.”
—David Hume (1711–1776)
“I happen to feel that the degree of a person’s intelligence is directly reflected by the number of conflicting attitudes she can bring to bear on the same topic.”
—Lisa Alther (b. 1944)
“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)