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:
“Again, the great number of cultivated men keep each other up to a high standard. The habit of meeting well-read and knowing men teaches the art of omission and selection.”
—Ralph Waldo Emerson (1803–1882)
“If matrimony be really beneficial to society, the custom that ... married women alone are allowed any claim to place, is as useful a piece of policy as ever was invented.... The ridicule fixed on the appellation of old maid hath, I doubt not, frightened a very large number into the bonds of wedlock.”
—Sarah Fielding (1710–1768)
“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)