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:
“I have known a number of Don Juans who were good studs and who cavorted between the sheets without a psychiatrist to guide them. But most of the busy love-makers I knew were looking for masculinity rather than practicing it. They were fellows of dubious lust.”
—Ben Hecht (1893–1964)
“Can it be, that the Greek grammarians invented their dual number for the particular benefit of twins?”
—Herman Melville (1819–1891)
“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)