Question 943261: A Dudley-brand lock is made of a 60-number dial (0, 1, 2, . . . , 59). To unlock it, one
must make the right sequence of 3 numbers in order. Turning the dial to clockwise to
the first number, then counterclockwise (a full turn and then continuing) to the second
number, then clockwise to the third number. There are conditions that a number
cannot be used twice in a row, and the next number cannot be one of the 2 immediate
neighbours (one to the left, one to the right). How many possible different arrangements
are there for a Dudley lock? (For example 59, 1, 59 is a possible arrangement.)
Answer by Fombitz(32388)   (Show Source):
You can put this solution on YOUR website! OK so the first number choice you have 60 choices.
The second number, you start with 60 choices but then subtract 3 for the previous number and its neighbors. So the second choice leaves you with 57 choices.
The third choice you start with 60 choices but then subtract 3 for the previous number and its neighbors.
So,
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