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I've wondered about the same thing of generating a permutation with a minimum number of samples. I'm not sure how Gray codes helps you here, and the multiplication sounds wrong since many outputs aren't reachable from any input.

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The idea is just a closed form solution that gets you from a number in 1...nPermutations to a single specific permutation. I was using Gray codes as an example of a sequence that exhausts all permutations with a closed form that gets you to a specific point in the sequence.

Might not work - as I say I never actually got around to implementing it.

I think you're looking for a factorial number system [1] and/or Lehmer code [2].

[1] https://en.wikipedia.org/wiki/Factorial_number_system [2] https://en.wikipedia.org/wiki/Lehmer_code

Thanks!

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