Introduction

Apparently, this is a known problem [1]. I had not seen this before, but it worked out pretty well. After drawing a couple of permutations on paper, I concluded that figuring out the permutations guess after guess does not seem realistic.

The remaining options:

1. Guess randomly. Success probablity: 0.5**100
2. Hope for small enough cycles in the permutation. Success probablity: ??? [1]

So I wrote a script [2] for option 2 as well as a bruteforcer script that would continuously launch my solver. Luckily, it worked out the very first time. :)

References

[1] http://robertheaton.com/2014/01/13/mathematicians-hate-civil-liberties-100-prisoners-100-boxes/

[2] https://gist.github.com/zku/d8869cbef6e7c1f614c7