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:
“Civilization is maintained by a very few people in a small number of places and we need only some bombs and a few prisons to blot it out altogether.”
—Cyril Connolly (1903–1974)
“I can’t quite define my aversion to asking questions of strangers. From snatches of family battles which I have heard drifting up from railway stations and street corners, I gather that there are a great many men who share my dislike for it, as well as an equal number of women who ... believe it to be the solution to most of this world’s problems.”
—Robert Benchley (1889–1945)
“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)