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:
“Even in ordinary speech we call a person unreasonable whose outlook is narrow, who is conscious of one thing only at a time, and who is consequently the prey of his own caprice, whilst we describe a person as reasonable whose outlook is comprehensive, who is capable of looking at more than one side of a question and of grasping a number of details as parts of a whole.”
—G. Dawes Hicks (1862–1941)
“In the U.S. for instance, the value of a homemaker’s productive work has been imputed mostly when she was maimed or killed and insurance companies and/or the courts had to calculate the amount to pay her family in damages. Even at that, the rates were mostly pink collar and the big number was attributed to the husband’s pain and suffering.”
—Gloria Steinem (20th century)
“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)