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:
“There is something tragic about the enormous number of young men there are in England at the present moment who start life with perfect profiles, and end by adopting some useful profession.”
—Oscar Wilde (1854–1900)
“It seems to me that there must be an ecological limit to the number of paper pushers the earth can sustain, and that human civilization will collapse when the number of, say, tax lawyers exceeds the world’s total population of farmers, weavers, fisherpersons, and pediatric nurses.”
—Barbara Ehrenreich (b. 1941)
“Science is feasible when the variables are few and can be enumerated; when their combinations are distinct and clear. We are tending toward the condition of science and aspiring to do it. The artist works out his own formulas; the interest of science lies in the art of making science.”
—Paul Valéry (1871–1945)