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:
“After mature deliberation of counsel, the good Queen to establish a rule and imitable example unto all posterity, for the moderation and required modesty in a lawful marriage, ordained the number of six times a day as a lawful, necessary and competent limit.”
—Michel de Montaigne (1533–1592)
“If matrimony be really beneficial to society, the custom that ... married women alone are allowed any claim to place, is as useful a piece of policy as ever was invented.... The ridicule fixed on the appellation of old maid hath, I doubt not, frightened a very large number into the bonds of wedlock.”
—Sarah Fielding (1710–1768)
“I had a quick grasp of the secret to sanity—it had become the ability to hold the maximum of impossible combinations in one’s mind.”
—Norman Mailer (b. 1923)