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:
“The two great points of difference between a democracy and a republic are: first, the delegation of the government, in the latter, to a small number of citizens elected by the rest; secondly, the greater number of citizens and greater sphere of country over which the latter may be extended.”
—James Madison (1751–1836)
“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)
“I had a quick grasp of the secret to sanity—it had become the ability to hold the maximum of impossible combinations in one’s mind.”
—Norman Mailer (b. 1923)