Quandaries and Queries


Here is my question: A combination lock has 60 positions arranged in a circle to which a pointer may be set.  Three settings are required to open it and no one setting may be closer than 5 positions from the immediately preceding setting.   How many different locks may be manufactured?


Hi Kathy,

How many ways for the first number? 60

How many for the second? You need to exclude 4 numbers before and after the one you just chose and also the one you just chose.

Now repeat your answer from the previous step and apply the multiplication principle.



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