Stuff on permutations that I've been playing with:
- The two permutations of the digits 1 and 2 are 12 and 21. The average of these numbers is 16.5
- The 6 permutations of the digits 1,2,3 are 123, 132, 213, 231, 312 and 321. Their average is 222.
Extending this: | Digits | N(permutations) | Average | Ratio to previous | | 1 | 1 | 1.0 | | 1,2 | 2 | 16.5 | 16.500 | | 1,2,3 | 6 | 222.0 | 13.455 | | 1,2,3,4 | 24 | 2777.5 | 12.511 | | 1,2,3,4,5 | 120 | 33333.0 | 12.001 | | 1,2,3,4,5,6 | 720 | 388888.5 | 11.667 | | 1,2,3,4,5,6,7 | 5040 | 4444444.0 | 11.429 | | 1,2,3,4,5,6,7,8 | 40320 | 49999999.5 | 11.250 |
Interesting isn't it? I reckon there's a theorum in here waiting to get out somewhere.
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