The order of a permutation is the number of times that permutation must be repeated until the objects return to their original positions. For example the permutation (2,3,1) on the letters ABC successively generates BCA, CAB and ABC, so its order is 3.
What is the highest possible order of a permutation on a list of 100 elements?
Once I realized that the order of a permutation is the LCM of all the cycle lengths, the obvious answer is to set as many cycle lengths to prime numbers as possible.
I stopped there and assumed the sum of the first consecutive several primes would most likely not be exactly 100, so the solution method would involve which non consecutive primes fit the bill or to maybe have a 1 or 2 left over, wasting a number.
But to my surprise, the sum of the first 9 primes is exactly 100.
So the answer is the product of the first 9 primes as others have shown.
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Posted by Larry
on 2024-01-24 12:16:56 |
my solution stream of consciousness
