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:
“A good marriage ... is a sweet association in life: full of constancy, trust, and an infinite number of useful and solid services and mutual obligations.”
—Michel de Montaigne (1533–1592)
“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)
“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)