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:
“That country is the richest which nourishes the greatest number of noble and happy human beings.”
—John Ruskin (1819–1900)
“I believe if we introduced the Lord’s Prayer here, senators would propose a large number of amendments to it.”
—Henry Wilson (1812–1875)
“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)