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I'm struggling to come up with examples. Maybe the 3n+1 problem? It's definitely easy to understand in a few seconds, and definitely fiendishly hard. I'm not s

I'm struggling to come up with examples. Maybe the 3n+1 problem? It's definitely easy to understand in a few seconds, and definitely fiendishly hard. I'm not sure if it seems easy to solve though :) Another one that came to mind is about efficiently computing the permanent of a matrix[1]. Maybe understandable in seconds if you know how determinants work. [1] https://en.wikipedia.org/wiki/Computing_the_permanent https://en.wikipedia.org/wiki/Computing_the_permanent

DataDaoDe 6y ago
3n + 1 is interesting because it seems so tantalizingly easy and beautiful at first glance. Its like looking at a stream where you can clearly see the stony bed and it appears to be ankle deep but once you take a step you realize the lighting has fooled you and you fall head over heels into icy waters.
- pas 6y ago
  It's so much more interesting if you happen to know about the "hydra game" (the Goodstein theorem), which is also a question about sequences and their termination at 0. https://en.wikipedia.org/wiki/Goodstein%27s_theorem https://en.wikipedia.org/wiki/Goodstein%27s_theorem But this is easily proved (using infinite ordinals, but it seems it could be proved just by coming up with a similar concept like the infinite ordinal arithmetic, basically providing an upper bound for each step of the algorithm and showing that there's an eventual maximum to these and then there's a monotonic decrease, and that the number of steps are always finite).