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:
“... is it not clear that to give to such women as desire it and can devote themselves to literary and scientific pursuits all the advantages enjoyed by men of the same class will lessen essentially the number of thoughtless, idle, vain and frivolous women and thus secure the [sic] society the services of those who now hang as dead weight?”
—Sarah M. Grimke (1792–1873)
“Take away from the courts, if it could be taken away, the power to issue injunctions in labor disputes, and it would create a privileged class among the laborers and save the lawless among their number from a most needful remedy available to all men for the protection of their business interests against unlawful invasion.... The secondary boycott is an instrument of tyranny, and ought not to be made legitimate.”
—William Howard Taft (1857–1930)
“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)