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 genius of democracies is seen not only in the great number of new words introduced but even more in the new ideas they express.”
—Alexis de Tocqueville (1805–1859)
“In the multitude of middle-aged men who go about their vocations in a daily course determined for them much in the same way as the tie of their cravats, there is always a good number who once meant to shape their own deeds and alter the world a little.”
—George Eliot [Mary Ann (or Marian)
“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)