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:
“It is always possible to bind together a considerable number of people in love, so long as there are other people left over to receive the manifestations of their aggression.”
—Sigmund Freud (1856–1939)
“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)
“What is the structure of government that will best guard against the precipitate counsels and factious combinations for unjust purposes, without a sacrifice of the fundamental principle of republicanism?”
—James Madison (1751–1836)