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:
“In proportion as our inward life fails, we go more constantly and desperately to the post office. You may depend on it, that the poor fellow who walks away with the greatest number of letters, proud of his extensive correspondence, has not heard from himself this long while.”
—Henry David Thoreau (1817–1862)
“While I do not suggest that humanity will ever be able to dispense with its martyrs, I cannot avoid the suspicion that with a little more thought and a little less belief their number may be substantially reduced.”
—J.B.S. (John Burdon Sanderson)
“You should try to understand every thing you see and hear; to act and judge for yourselves; to remember you each have a soul of your own to account for; M a mind of your own to improve. When you once get these ideas fixed, and learn to act upon them, no man or set of men, no laws, customs, or combinations of them can seriously oppress you.”
—Jane Grey Swisshelm (1815–1884)