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.
Read more about this topic: Dogic
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)
“My idea is that the world outside—the so-called modern world—can only pervert and degrade the conceptions of the primitive instinct of art and feeling, and that our only chance is to accept the limited number of survivors—the one- in-a-thousand of born artists and poets—and to intensify the energy of feeling within that radiant centre.”
—Henry Brooks Adams (1838–1918)
“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)