Saturday, 3 February 2018

The Permutations of {1, 2, 3, 4, 5}

Today I am 25143 days old, a permutation of the digits 1, 2, 3, 4 and 5. There are 5! or 120 possible ways to arrange these digits and they are as follows:

{1, 2, 3, 4, 5} | {1, 2, 3, 5, 4} | {1, 2, 4, 3, 5} | {1, 2, 4, 5, 3} | {1, 2, 5, 3, 4} | {1, 2, 5, 4, 3} | {1, 3, 2, 4, 5} | {1, 3, 2, 5, 4} | {1, 3, 4, 2, 5} | {1, 3, 4, 5, 2} | {1, 3, 5, 2, 4} | {1, 3, 5, 4, 2} | {1, 4, 2, 3, 5} | {1, 4, 2, 5, 3} | {1, 4, 3, 2, 5} | {1, 4, 3, 5, 2} | {1, 4, 5, 2, 3} | {1, 4, 5, 3, 2} | {1, 5, 2, 3, 4} | {1, 5, 2, 4, 3} | {1, 5, 3, 2, 4} | {1, 5, 3, 4, 2} | {1, 5, 4, 2, 3} | {1, 5, 4, 3, 2} | {2, 1, 3, 4, 5} | {2, 1, 3, 5, 4} | {2, 1, 4, 3, 5} | {2, 1, 4, 5, 3} | {2, 1, 5, 3, 4} | {2, 1, 5, 4, 3} | {2, 3, 1, 4, 5} | {2, 3, 1, 5, 4} | {2, 3, 4, 1, 5} | {2, 3, 4, 5, 1} | {2, 3, 5, 1, 4} | {2, 3, 5, 4, 1} | {2, 4, 1, 3, 5} | {2, 4, 1, 5, 3} | {2, 4, 3, 1, 5} | {2, 4, 3, 5, 1} | {2, 4, 5, 1, 3} | {2, 4, 5, 3, 1} | {2, 5, 1, 3, 4}

TODAY | {2, 5, 1, 4, 3} | 

{2, 5, 3, 1, 4} | {2, 5, 3, 4, 1} | {2, 5, 4, 1, 3} | {2, 5, 4, 3, 1} | {3, 1, 2, 4, 5} | {3, 1, 2, 5, 4} | {3, 1, 4, 2, 5} | {3, 1, 4, 5, 2} | {3, 1, 5, 2, 4} | {3, 1, 5, 4, 2} | {3, 2, 1, 4, 5} | {3, 2, 1, 5, 4} | {3, 2, 4, 1, 5} | {3, 2, 4, 5, 1} | {3, 2, 5, 1, 4} | {3, 2, 5, 4, 1} | {3, 4, 1, 2, 5} | {3, 4, 1, 5, 2} | {3, 4, 2, 1, 5} | {3, 4, 2, 5, 1} | {3, 4, 5, 1, 2} | {3, 4, 5, 2, 1} | {3, 5, 1, 2, 4} | {3, 5, 1, 4, 2} | {3, 5, 2, 1, 4} | {3, 5, 2, 4, 1} | {3, 5, 4, 1, 2}

JUST BEFORE | {3, 5, 4, 2, 1} | 97th BIRTHDAY

{4, 1, 2, 3, 5} | {4, 1, 2, 5, 3} | {4, 1, 3, 2, 5} | {4, 1, 3, 5, 2} | {4, 1, 5, 2, 3} | {4, 1, 5, 3, 2} | {4, 2, 1, 3, 5} | {4, 2, 1, 5, 3} | {4, 2, 3, 1, 5} | {4, 2, 3, 5, 1} | {4, 2, 5, 1, 3} | {4, 2, 5, 3, 1} | {4, 3, 1, 2, 5} | {4, 3, 1, 5, 2} | {4, 3, 2, 1, 5} | {4, 3, 2, 5, 1} | {4, 3, 5, 1, 2} | {4, 3, 5, 2, 1} | {4, 5, 1, 2, 3} | {4, 5, 1, 3, 2} | {4, 5, 2, 1, 3} | {4, 5, 2, 3, 1} | {4, 5, 3, 1, 2} | {4, 5, 3, 2, 1} | {5, 1, 2, 3, 4} | {5, 1, 2, 4, 3} | {5, 1, 3, 2, 4} | {5, 1, 3, 4, 2} | {5, 1, 4, 2, 3} | {5, 1, 4, 3, 2} | {5, 2, 1, 3, 4} | {5, 2, 1, 4, 3} | {5, 2, 3, 1, 4} | {5, 2, 3, 4, 1} | {5, 2, 4, 1, 3} | {5, 2, 4, 3, 1} | {5, 3, 1, 2, 4} | {5, 3, 1, 4, 2} | {5, 3, 2, 1, 4} | {5, 3, 2, 4, 1} | {5, 3, 4, 1, 2} | {5, 3, 4, 2, 1} | {5, 4, 1, 2, 3} | {5, 4, 1, 3, 2} | {5, 4, 2, 1, 3} | {5, 4, 2, 3, 1} | {5, 4, 3, 1, 2} | {5, 4, 3, 2, 1}

Humans will only experience up to 35421 because 35421/365.25 = 96.98 or about 8 days short of one's 96th birthday. The next number 41235 is only reached a little short of one's 113th birthday. There's nothing deeply mathematical about any of this and of course it's specific to the number system being used. For example, in an octal base 25143 becomes 61067\(_8 \). Primeness of course is different and transcends number systems. 61067\(_8 \) and 25143\(_{10} \) are both prime!

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