June 17th, 2021

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Solutions and discussion of yesterday's logic puzzles

This post is for discussion and solutions to the hard logic puzzles in my previous post. I recommend reading that one first, especially if you want to think about the puzzles without spoilers.
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I feel like there should be some practical application here - some similar real-world situation where it looks at first and second glance like there's zero information that can be conveyed, but where a clever strategy means that actually it can, and the discrepancy between the apparent security and the actual information leak can be exploited.

I don't necessarily mean "exploited" in an immoral way: it could be an attack against economic deadweight loss, or against Moloch (Scott Alexander's term for tragedy-of-the-commons type situations where the sum of everyone's actions leads to a situation nobody wants but no individual can break the deadlock), or against entropy (in the sense of general chaos and decay, not in the information-theory-specific sense, confusingly), rather than against other people. Finding information leaks in apparently secure contexts sounds like the domain of fraudsters and hackers, but it could also be applied to things like reconstructing fragmentary ancient texts or recovering corrupted recordings that seem to be lost, or providing market information that was thought to be unknowable but which is useful to both buyers and sellers - or, of course, white-hat hacking, finding potential exploits for fraudsters and hackers and closing them.